From 7d1f69d077ed19f22d669db984bcfa97c1e0544b Mon Sep 17 00:00:00 2001 From: Thomas Fenz Date: Wed, 24 Jun 2020 18:38:01 +0200 Subject: [PATCH 01/12] added post aalwines + image --- _posts/2020-06-24-aalwines.md | 140 ++++++++++++++++++++++++++ assets/images/aalwines-screenshot.png | Bin 0 -> 1090348 bytes 2 files changed, 140 insertions(+) create mode 100644 _posts/2020-06-24-aalwines.md create mode 100644 assets/images/aalwines-screenshot.png diff --git a/_posts/2020-06-24-aalwines.md b/_posts/2020-06-24-aalwines.md new file mode 100644 index 0000000..ef6abc6 --- /dev/null +++ b/_posts/2020-06-24-aalwines.md @@ -0,0 +1,140 @@ +--- +layout: post +title: "AalWiNes" +authors: [Stefan Schmid, ] +categories: [research, network, verification] +image: assets/images/aalwines-screenshot.png +tags: [] +--- + +With the increasing scale of communication networks, +failures (e.g. link failures) are becoming the norm rather than the +exception. Given the critical role such networks play for our +digital society, it is important to ensure a reliable and +efficient operation of such networks, even in the presence +of one or multiple failures. +While several interesting automated approaches to +verify and operate networks are emerging, providing an attractive +alternative to today’s pragmatic and manual “fix it when it breaks” approach, existing solutions often only provide a limited and inefficient +support for reasoning about failure +scenarios. In particular, many of these solutions +essentially require to test each possible failure scenario +one-by-one. +The resulting runtime is exponential in the number of failures, $k$, +which makes this approach not very well-suited for testing +large-scale communication networks. + +## A case for verifying network configurations + +It is often attractive to verify the +network configuration directly: compared to verifying +control plane protocols, analyzing the dataplane +configuration (e.g., forwarding and conditional +failover tables) has the advantage that it +also accounts for possible external changes, +e.g., manual changes through the CLI, bugs, or +changes made by +additional prototcols. Moreover, this approach can also reveal +problems in the network operation introduced by the algorithms +that generate the routing tables from the control plane specifications. +In our work we focus on the verification of forwarding rules +in MPLS routing tables. In MPLS, packet labels can be nested +in order to provide tunneling through the network or to handle link +failures by fast-reroute mechanism. This mechanism relies on pushing a new MPLS +label on top of the label stack, to redirect the flow +to go around the failed link. This mechanism can be applied several times +in case of multiple link failures, creating larger and larger (in theory: unbounded) +numbers of MPLS labels on the label-stack. + +To this end, we have developed a tool called P-Rex [[1]](#references) +in Python, that has been recently reimplemented in C++ and integrated into +the AalWiNes [project website](https://github.com/DEIS-Tools/AalWiNes-Web) network verification suit developed jointly +by researchers at Aalborg University and the University of Vienna. +Our tool is currently tailored towards MPLS and Segment Routing (SR) networks, exploiting +that their routing and failover behavior is based on stacks of labels. +The tool allows to verify a +wide range of important network properties in polynomial time, +parameterized by the maximum number of assumed link failures. +At the core of the tool lies an expressive query language for reachability +analysis, based on regular expressions, both to specify packet headers as well +as constraints on the routes. Specifically, queries are of the form: + +$ < a > b < c > k $ + +where $a$ and $c$ are regular expressions over MPLS labels that describe the +set of allowed initial resp. final headers of packets in the +trace, $b$ is a regular expression over the links in the network, defining the set +of allowed routing traces through the network, and $k$ is a number +specifying the maximum number of failed links to be accounted for. + + +By using regular expressions, we can +test properties such as waypoint enforcement (e.g., is the +traffic always forwarded through an intrusion detection system) +or avoidance of certain routers in selected countries. +The tool also allows to account for more complex +traffic engineering aspects, such as load-balancing, by supporting +nondeterminism, as well as more complex multi-operation chains. + +## How does polynomial-time what-if analysis work? + +The model checking algorithm relies on an automata-theoretic approach +and leverages a natural (but not +well-known) connection to the theory of pushdown automata and +prefix rewriting systems. +In a nutshell, given the network configuration, the routing tables, +as well as the query, the tool constructs a pushdown automaton +(PDA). This PDA is then an input for the backend tool (earlier we used Moped, +more recently we have developed our own dedicated verification engine) +that is used for reachability analysis. In more details, +the regular expressions for the initial header and the final +header of the query are each converted to first a +Nondeterministic Finite Automaton (NFA) and then to a Pushdown +Automaton (PDA). The path query is converted to an NFA, which is +used to restrict (by synchronous product) +the behaviour of the PDA constructed based on the network model. +The three PDAs are combined into a single PDA that we give to +to the backend engine that checks the emptiness of the PDA language. +In case the language is nonempty, the tool returns a witness trace +to demonstrate the reason why the query is satisfied. Otherwise the +answer is that the query is not satisfied. +In the most recent extension, we modify the witness trace generation +so that we can generate (among a possibly infinite number of witness traces) +the ones that minimize certain criteria (e.g. the number of hops, latency, +and the stack height that corresponds to the number of tunnels). This is +achieved by extending the PDA reachability analysis with multi-dimensional weights. +Despite the added complexity, the verification can be still performed in polynomial time. + +The tool includes several optimizations to +further improve the performance, such as “top of stack reduction”, +which safely calculates which labels can be at the top of stack in a +given state of the PDA: the top of stack reduction technique greatly +reduces the amount of transitions in the PDA. + +## Example + +To be more concrete, our tool allows to load an arbitrary network +topology (e.g., from the topology zoo dataset) as well +as a set of router configurations (e.g., from Juniper routers). +The configurations are then put into an standardized, intermediate +format which is vendor independent. The user can then define +a query (see above), which leads the tool to prompt with a result +(e.g. a trace). +Here is an example screenshot of our tool: ![Alt](/assets/images/aalwines-screenshot.png "AalWiNes") + + +We refer to our [tool website](https://whatif-tools.net/) as well as to our +[project website](https://github.com/DEIS-Tools/AalWiNes-Web). + +## Conclusion and future work + +We consider providing a low runtime critical for the success of network +verification, and reasoning about failures seems particularly challenging. +We hence hope that our approach, which is specific to MPLS and Segment Routing networks, +will inspire the community to conduct more research on the feasiblity +of fast and polynomial time what-if analysis algorithms, also for other network types +and control plane protocols. + +## References + +\[1\] : P-Rex: Fast Verification of MPLS Networks with Multiple Link Failures. Jesper Stenbjerg Jensen, Troels Beck Krogh, Jonas Sand Madsen, Stefan Schmid, Jiri Srba, and Marc Tom Thorgersen. 14th ACM International Conference on emerging Networking EXperiments and Technologies (CoNEXT), Heraklion/Crete, Greece, December 2018. \ No newline at end of file diff --git a/assets/images/aalwines-screenshot.png b/assets/images/aalwines-screenshot.png new file mode 100644 index 0000000000000000000000000000000000000000..3376afba8aa507cb22260cc0678c0a1bcbf0d3a7 GIT binary patch literal 1090348 zcmaHS1y~$S@;49?AOv>^?(XjHPH=ZyJh%jR4;I`Vf;$9vcNR%-cU@Tcc<=6e?~?y> zH_yy=O)FDfUG?j#CR|BD65&1Wdk6>!1ZgQT6$l9U83+iN1lV`4ISZ2X+Yk`%SFA)u zm83;QiIkk|&8=+BARwf|lTu(bRkbh&&%8>5f*|~*D6iLbAWCzCNu*$u;iQRjgW{0Y z`X+wD#=J#Ap?kwallOC9sV_wHJIT@`G|Jo0_;gE3b&TJG(w6Pry7(XLP8s(yy-vCB zI_`X4AcWqVzy-H_r-ASY5K*?ZB%AvvPd(C$}Y!K&Sn6h8rLQG>`%tkC}NfG3=!$?AgG72?A8yRrK_6y&0 z^)z~TJU9_ZETM*DK?#W{z)Z0|e`P&ld|*X?(5j$&t9Z+9bWhZ&nL4U{?ME>F(%7y$ zJV&rQM06=;RC5WAyJ|~MB+NAw9;n!--gTz1Nnlk(O=jx1WhVU`!CjF9+rP4^6|b5x zjATS}iO#ZBoJxxrlWwf+TVY%+heB!?p_Lcz0|zTh&JFioFm_aJn{l_FQr;0o&~X7h z(s`4l$OQX+mlSGwNj5DkLdH6$*tA#Hy(0KBEutZ~{hmqutl|LF67c09W7AX|@X=1` z+(j;cL|+rTWJxv^FF$N=H-zSCGmoo(MP&O|hCW_CSFf$Q`xyEgfiNh#A4T!SuwO(@ zdqg})qr88Spa@24NWlxOb1+0x8v=nd8Tgs_ka1mYiLt%Bhkd+o%8c@l>J3moomD6j z@zZa`Z6SV!y>-$775QM|K@uH7Ipk*1qhQE`rY;#jINc2iy|H}r#t@3mAK&5K=?}d7 zKtp82JYha5$g4PQ4R(utAUVE_=U^T~xBU=sK>qmd+V z(iij({wap&-Vj^J(7%XK#r*4uMTb7r`ezXHY{S15jaQ=k3RNho6$ga>VpBcg+0-oZxguwM*7cnqImkVMy^jZ4o`sKg@;v?i>uk$auW(bB5* z5LO`wzW{&Eo}1lc(ghpzm{5IDkx*8apyEZx?-vr!S5Z!*Lb0YU`}ir^T8KTLN149_ zkBa&bD z1x{kH))(qtHIrLIZRS0uCMMBTBu%>Hh=w1YhP~gZmu!!XkF}3oZQ&c?fwA~~F~1zR z02v4qFj&zhzur5VHCHyjX;y7MY9?N#Y-d?VK8r%?F5Y~5pLB2iFPcg9 zU0OzsDrJEJZ($Fi2Ug`wOLEMFT1rjqjGbS^X z7!eU2?^T2IYvl?R3gvfNM{H_Qm!m!kWl1tnXe7qQRmU5Y(v*HHXHnBCll^q07F)Ki zjIWws!d)s}zEfKH30Uo_4A8_cwyPqjm{4Z?v{C3Q;S(2-m#Tz~&S8dO#<}y+OzKU! zQEvC#&_c-+SIKlab6IKCL0MW!i&CA!RZ!8_h`evAX>+=Vo`*(Cm>aVip@8pzyslzx5N#xF6m5`RWj+O9 znMc>hMZ_Y+Qbas_&yStFt=zjjr>@>V3r^8b>t{-54=U>#Sb;4Q4@L09;FU4xB!NP0Lz){G8Wm&YV_Et@6p6VB^U`ofySR>COb7vl4VCaAb*_^egudbP~! zpzBuhh1pm=Rj>20BU1xXP3mguOw1R@eKC*Fbx?t5lHuuuO@gPQ-iA-0dl*@+i^*1(jfoV1LCSS)5?Txy&@14uINOcMA$nQLg z6wS?c9g-CniYidD2&=!{MNIx&yxcGiH9H%7PDRVCooCXYQb3o8`;r53v*wWGPMuf$Y*_(#GQ@*COQLLAw)lr%b8J&t-lmxoS_APjEW zswx*$Zz-)YhePfh+CxzxC zZ5eH6m05Mib>gfdyWsGGS=Eu=S*P#dyW@A=AwWDZ$7#7*IbGGqRrH3^$_VvO`ZvB; zPvcnSdgX3*#J2Ia@e5)LF1GAztwu+S+WIGztv_0m0iM7G+sEe2Ixq5}zjuk9xH27s`OFyHpQEy9%_nAzO6hXrDc_HwyZJAP=?_^#2)=(@2i5j!vd_IzCA z?3Pa`ihpAT144XD%+sNiRxhTkKRU+l%=vuu)yc#shDz zu>??`xyW!Lb+9jp>s#M8+g5jz3a;rGjE-5%oZ_o_Ci`W2AiZ3=scNFvQ>9T{r-0-- zdFJat@h~=CS2uZ^70KoH%X{d7l^>G7nBiWR%Xj){b6WOV_9SJEu}ROdZN_u{#M-9X z%O1!cYlH8T<&z0!eN@!HYx4z3OhsRDrg1WEeEVGf;@Wf4<~DOGb>?)6xG~ysx9d9% zzJM7eG$u$ERPj**Yo0mwo~d^=Nv#!9z6*F)#TV{%X&A?Ue_48eu$VhzQD8AYiIB~S z$cscs2#0gv#k|))CHrgiLc{Du>2a`eF}d3BvG*mGHh(x@)LzWq)PAvZ*0<@dQ@4Oi0s^*1@?hAOk82$7Z# z=Bx8hWl_%xp*uhAIZE$d=C(F0h^l{JJo!9RI^^Mfl=(*3`3iO;%rvFV<>eu0UTIhe zXh>X$x33iB>mvY(_ctv8Nd@udANf!a5TRBO(EqBV@S6U0#l1d%wfSfICLsg@=JgHr z^>NRE`v0}zXL8>Be;Ov?wG2X7Ra9E~HB~inGBdMtwzPNIq(W|g&46=|(sG7?z$E|c zfs|GuJAdte$x2PrMN?jm$HX4MU}S1d zE-nr{jErt>ZVYa$4E9bIjLh8J+>A^tj4UkluQlkMJ?vbJ-0AI{N&nf&|L;f4%-O`r z%E86T-j3+6evORnKfCagko+~!-`79?PBV9_e~)D6{IAb?{XoXQN*I|Lm>B==`?V?G zU%5O=R_s|^QlDNc#_8RarZC? zxg!%jfr2-*?9DyB-MYfYqRJ``53{OH37W2|GfzgwMxvsglG3s&{KU-`>{=@1G=(6b z|JVJKjUsM*r-Z4w=>R2pl-wj=mm#sJkSKBZT_bCnTwJnet0mZ7Z}_f4Q!!09S*9>g zeGnH~$WQ?7r?Z!}bq0kbJR7%wO#d)54MuU);Ib~>&PrQJM|tSWUTI~eCP!=~xNH#;m{$QKcAs6}dr4g>MD>M*!;tI@T3 zb*R+1|3RmLnd6HP8g$Vke*R*{dPBM%4Y!UxKAJr~}$ZxqOsGCmfEPZQ%ZX5^KI zE00_RGI3KTGuA@1Y0@d{NOFGOg(=BzO9{To9Ekb2MGA9Az9OfC-PLI6)iGe%nfBRt zoPzX_VRF`489IN*I4$Iz8wDb3x> z_{cFYeva!G*3%SteT-5

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insertion(+), 1 deletion(-) diff --git a/_posts/2020-06-24-aalwines.md b/_posts/2020-06-24-aalwines.md index ef6abc6..dbfe6a7 100644 --- a/_posts/2020-06-24-aalwines.md +++ b/_posts/2020-06-24-aalwines.md @@ -1,7 +1,7 @@ --- layout: post title: "AalWiNes" -authors: [Stefan Schmid, ] +authors: [Stefan Schmid, Jiri Srba] categories: [research, network, verification] image: assets/images/aalwines-screenshot.png tags: [] From f1b0d3f6d5d346902865fe1e59dafadfef42129f Mon Sep 17 00:00:00 2001 From: Thomas Fenz Date: Wed, 24 Jun 2020 19:15:04 +0200 Subject: [PATCH 03/12] minor changes: modified title, removed linebreak --- _posts/2020-06-24-aalwines.md | 5 ++--- 1 file changed, 2 insertions(+), 3 deletions(-) diff --git a/_posts/2020-06-24-aalwines.md b/_posts/2020-06-24-aalwines.md index dbfe6a7..d1b1f69 100644 --- a/_posts/2020-06-24-aalwines.md +++ b/_posts/2020-06-24-aalwines.md @@ -1,6 +1,6 @@ --- layout: post -title: "AalWiNes" +title: "AalWiNes: Automated and Polynomial-time What-if Analysis for MPLS Networks" authors: [Stefan Schmid, Jiri Srba] categories: [research, network, verification] image: assets/images/aalwines-screenshot.png @@ -68,8 +68,7 @@ of allowed routing traces through the network, and $k$ is a number specifying the maximum number of failed links to be accounted for. -By using regular expressions, we can -test properties such as waypoint enforcement (e.g., is the +By using regular expressions, we can test properties such as waypoint enforcement (e.g., is the traffic always forwarded through an intrusion detection system) or avoidance of certain routers in selected countries. The tool also allows to account for more complex From 9dfb4cc261d830f425cf6822d3ae1678cdf20d30 Mon Sep 17 00:00:00 2001 From: Thomas Fenz Date: Thu, 25 Jun 2020 09:32:03 +0200 Subject: [PATCH 04/12] embedded quick intro video; added authors and their avatars --- _config.yml | 14 ++++++++++++++ _posts/2020-06-24-aalwines.md | 4 ++-- assets/images/schmid.jpg | Bin 0 -> 27703 bytes assets/images/srba.jpg | Bin 0 -> 29534 bytes 4 files changed, 16 insertions(+), 2 deletions(-) create mode 100644 assets/images/schmid.jpg create mode 100644 assets/images/srba.jpg diff --git a/_config.yml b/_config.yml index 477655e..0cce599 100644 --- a/_config.yml +++ b/_config.yml @@ -81,6 +81,20 @@ authors: avatar: /assets/images/tim-thijm.jpg bio: "Tim is a PhD candidate at Princeton University, where he is currently advised by Prof. Aarti Gupta. Tim completed his BSc at the University of Toronto in 2018 in Computer Science and English." + schmid: + name: Stefan Schmid + site: https://www.univie.ac.at/ct/stefan/ + avatar: /assets/images/schmid.jpg + bio: "Stefan Schmid is a Full Professor at the University of Vienna, Austria. MSc and PhD at ETH Zurich, Postdoc at TU Munich and University of Paderborn, Senior Research Scientist at T-Labs in Berlin, and Associate Professor at Aalborg University, Denmark. Stefan Schmid is interested in the fundamental and algorithmic problems underlying networked systems. He received the IEEE Communications Society ITC Early Career Award 2016 and an ERC Consolidator Grant 2019. +" + + srba: + name: Jiri Srba + site: http://people.cs.aau.dk/~srba/ + avatar: /assets/images/srba.jpg + bio: "Jiri Srba is a Full Professor in computer science at Aalborg University, Denmark. He holds MSc from Faculty of Informatics, Masaryk University in Brno and PhD degree from Aarhus University. Since 2005, he has been employed at Aalborg University. Jiri Srba is interested in applying formal methods such as model checking into industrial cases from computer networking, supervisory control and wireless adhoc networks. +" + # Defaults defaults: diff --git a/_posts/2020-06-24-aalwines.md b/_posts/2020-06-24-aalwines.md index d1b1f69..5d6946c 100644 --- a/_posts/2020-06-24-aalwines.md +++ b/_posts/2020-06-24-aalwines.md @@ -1,7 +1,7 @@ --- layout: post title: "AalWiNes: Automated and Polynomial-time What-if Analysis for MPLS Networks" -authors: [Stefan Schmid, Jiri Srba] +authors: [schmid, srba] categories: [research, network, verification] image: assets/images/aalwines-screenshot.png tags: [] @@ -119,7 +119,7 @@ The configurations are then put into an standardized, intermediate format which is vendor independent. The user can then define a query (see above), which leads the tool to prompt with a result (e.g. a trace). -Here is an example screenshot of our tool: ![Alt](/assets/images/aalwines-screenshot.png "AalWiNes") +Here is an quick intro to our tool: [![AalWiNes Quick Intro](http://img.youtube.com/vi/mvXAn9i7_Q0/0.jpg)](http://www.youtube.com/watch?v=mvXAn9i7_Q0 "AalWiNes Quick Intro") We refer to our [tool website](https://whatif-tools.net/) as well as to our diff --git a/assets/images/schmid.jpg b/assets/images/schmid.jpg new file mode 100644 index 0000000000000000000000000000000000000000..50d2e9ad74a13b0aa7a372a9d071124b6e4663e8 GIT binary patch literal 27703 zcmbTd1yCGOuqe8?E-ncnIE3Kt?vUW_!DVrG3Bj{y@DL<8Ebf}%7Ibm<;O_R9TzU6b zy?X!Gn_{QV%=GDF?cF@jKCb}`q`hn`0RVY<1^_Am0DuFeeuf9|!dfJ--^)eue|5d| zd_Dl+O1YbXykS@oVb9{QS8E8H)^2W20<5eKt}G_zj;0nYW{&o(UM5bg>?~}o03lH? zClfP}g&T#bg_VtiFx7EO2Ni{lxiFPBw<4ROlca^Ujhv5*g}RTDhM5n@jNhC}RD?pv 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-1,6 +1,7 @@ --- layout: post -title: "AalWiNes: Automated and Polynomial-time What-if Analysis for MPLS Networks" +title: "Toward Polynomial-Time Verification of Networks with Infinite State Space: An Automata-Theoretic Approach" +subtitle: "The AalWiNes What-if Analysis Suite" authors: [schmid, srba] categories: [research, network, verification] image: assets/images/aalwines-screenshot.png @@ -14,19 +15,16 @@ digital society, it is important to ensure a reliable and efficient operation of such networks, even in the presence of one or multiple failures. While several interesting automated approaches to -verify and operate networks are emerging, providing an attractive +verify and operate networks are emerging, offering an attractive alternative to today’s pragmatic and manual “fix it when it breaks” approach, existing solutions often only provide a limited and inefficient support for reasoning about failure -scenarios. In particular, many of these solutions -essentially require to test each possible failure scenario -one-by-one. -The resulting runtime is exponential in the number of failures, $k$, -which makes this approach not very well-suited for testing -large-scale communication networks. +scenarios. In particular, verifying networks is a complex task, even for computers. For example, many existing automated solutions require to test each possible failure scenario (respectively, each possible dataplane) individually, resulting in a runtime which can be exponential in the number of failures, k; which makes this approach impractical for large-scale communication networks. In fact, certain communication networks, such as networks based on MultiPath Label Switching (MPLS) or Segment Routing (SR), may even have a theoretically infinite configuration space: in MPLS and SR networks, default routes as well as failover routes depend on the label stack in the packet header, which may grow and shrink arbitrarily along the route. + +In this article, we argue that automata-theoretic approaches can offer an interesting solution to these problems, allowing to perform fast verification, accounting even for failure scenarios and dealing with potentially infinite state spaces. ## A case for verifying network configurations -It is often attractive to verify the +Before delving into the details, we first argue that it is often attractive to verify the network configuration directly: compared to verifying control plane protocols, analyzing the dataplane configuration (e.g., forwarding and conditional @@ -34,11 +32,12 @@ failover tables) has the advantage that it also accounts for possible external changes, e.g., manual changes through the CLI, bugs, or changes made by -additional prototcols. Moreover, this approach can also reveal +additional prototcols. Moreover, dataplane-based approaches can also reveal problems in the network operation introduced by the algorithms that generate the routing tables from the control plane specifications. -In our work we focus on the verification of forwarding rules -in MPLS routing tables. In MPLS, packet labels can be nested + +Let us consider the verification of forwarding rules in MPLS routing tables as an example. +In a nutshell, in MPLS, packet labels can be nested in order to provide tunneling through the network or to handle link failures by fast-reroute mechanism. This mechanism relies on pushing a new MPLS label on top of the label stack, to redirect the flow @@ -46,22 +45,11 @@ to go around the failed link. This mechanism can be applied several times in case of multiple link failures, creating larger and larger (in theory: unbounded) numbers of MPLS labels on the label-stack. -To this end, we have developed a tool called P-Rex [[1]](#references) -in Python, that has been recently reimplemented in C++ and integrated into -the AalWiNes [project website](https://github.com/DEIS-Tools/AalWiNes-Web) network verification suit developed jointly -by researchers at Aalborg University and the University of Vienna. -Our tool is currently tailored towards MPLS and Segment Routing (SR) networks, exploiting -that their routing and failover behavior is based on stacks of labels. -The tool allows to verify a -wide range of important network properties in polynomial time, -parameterized by the maximum number of assumed link failures. -At the core of the tool lies an expressive query language for reachability -analysis, based on regular expressions, both to specify packet headers as well -as constraints on the routes. Specifically, queries are of the form: +A fairly general query language which supports to reason about network behavior under failures could be based on regular expressions: $ < a > b < c > k $ -where $a$ and $c$ are regular expressions over MPLS labels that describe the +Here $a$ and $c$ are regular expressions over MPLS labels that describe the set of allowed initial resp. final headers of packets in the trace, $b$ is a regular expression over the links in the network, defining the set of allowed routing traces through the network, and $k$ is a number @@ -71,68 +59,74 @@ specifying the maximum number of failed links to be accounted for. By using regular expressions, we can test properties such as waypoint enforcement (e.g., is the traffic always forwarded through an intrusion detection system) or avoidance of certain routers in selected countries. -The tool also allows to account for more complex -traffic engineering aspects, such as load-balancing, by supporting -nondeterminism, as well as more complex multi-operation chains. ## How does polynomial-time what-if analysis work? -The model checking algorithm relies on an automata-theoretic approach -and leverages a natural (but not -well-known) connection to the theory of pushdown automata and -prefix rewriting systems. +In order to evaluate such queries and conduct what-if analysis quickly, we make the case for a model-checking algorithm +which is based on automata theory. Our approach is motivated by a natural (but not well-known) connection to the theory +of pushdown automata and prefix rewriting systems. In a nutshell, given the network configuration, the routing tables, -as well as the query, the tool constructs a pushdown automaton -(PDA). This PDA is then an input for the backend tool (earlier we used Moped, -more recently we have developed our own dedicated verification engine) -that is used for reachability analysis. In more details, +as well as the query, a pushdown automaton (PDA) can be constructed. +On this PDA, we can then perform a standard reachability analysis. In more details, the regular expressions for the initial header and the final -header of the query are each converted to first a +header of the query can each be converted to first a Nondeterministic Finite Automaton (NFA) and then to a Pushdown -Automaton (PDA). The path query is converted to an NFA, which is -used to restrict (by synchronous product) +Automaton (PDA). The path query is converted to an NFA, which can then be used to restrict (by synchronous product) the behaviour of the PDA constructed based on the network model. -The three PDAs are combined into a single PDA that we give to +The three PDAs can be combined into a single PDA that we can give to the backend engine that checks the emptiness of the PDA language. -In case the language is nonempty, the tool returns a witness trace -to demonstrate the reason why the query is satisfied. Otherwise the -answer is that the query is not satisfied. -In the most recent extension, we modify the witness trace generation -so that we can generate (among a possibly infinite number of witness traces) -the ones that minimize certain criteria (e.g. the number of hops, latency, -and the stack height that corresponds to the number of tunnels). This is -achieved by extending the PDA reachability analysis with multi-dimensional weights. -Despite the added complexity, the verification can be still performed in polynomial time. - -The tool includes several optimizations to -further improve the performance, such as “top of stack reduction”, -which safely calculates which labels can be at the top of stack in a -given state of the PDA: the top of stack reduction technique greatly -reduces the amount of transitions in the PDA. - -## Example - -To be more concrete, our tool allows to load an arbitrary network -topology (e.g., from the topology zoo dataset) as well -as a set of router configurations (e.g., from Juniper routers). -The configurations are then put into an standardized, intermediate -format which is vendor independent. The user can then define -a query (see above), which leads the tool to prompt with a result -(e.g. a trace). -Here is an quick intro to our tool: [![AalWiNes Quick Intro](http://img.youtube.com/vi/mvXAn9i7_Q0/0.jpg)](http://www.youtube.com/watch?v=mvXAn9i7_Q0 "AalWiNes Quick Intro") +In case the language is nonempty, we can return a witness trace +to demonstrate the reason why the query is satisfied. All these operations can be performed in polynomial time, +leveraging a classic result by J. Büchi. + +## The AalWiNes Tool and Example + +As a case study and to explore the feasibility of such an automata-theoretic approach, +we developed a framework, the AalWiNes suite, which allows to load an arbitrary network topology +(e.g., from the topology zoo dataset) as well as a set of router configurations (e.g., from Juniper routers). +The configurations are then put into a standardized, intermediate format which is vendor independent. +The user can then define a query as described above, which leads the tool to prompt with a result +(e.g. a trace). AalWiNes is a joint work at Aalborg University and the University of Vienna. + +For MPLS specifically, we have developed the P-Rex tool [[1]](#references), recently reimplemented in C++. +The tool allows to verify a wide range of important network properties in polynomial time, +parameterized by the $k$. +Here is a quick intro to our tool: + +[![AalWiNes Quick Intro](http://img.youtube.com/vi/mvXAn9i7_Q0/0.jpg)](http://www.youtube.com/watch?v=mvXAn9i7_Q0 "AalWiNes Quick Intro") +P-Rex also allows to account for more complex traffic engineering aspects, such as load-balancing, +by supporting nondeterminism, as well as +more complex multi-operation chains. +The tool includes several optimizations to further improve the performance, such as “top of stack reduction”, +which safely calculates which labels can be at the top of stack in a given state of the PDA: the top of stack +reduction technique greatly reduces the amount of transitions in the PDA. We refer to our [tool website](https://whatif-tools.net/) as well as to our [project website](https://github.com/DEIS-Tools/AalWiNes-Web). ## Conclusion and future work -We consider providing a low runtime critical for the success of network -verification, and reasoning about failures seems particularly challenging. -We hence hope that our approach, which is specific to MPLS and Segment Routing networks, -will inspire the community to conduct more research on the feasiblity -of fast and polynomial time what-if analysis algorithms, also for other network types -and control plane protocols. +We consider providing a low runtime critical for the success of network verification, +and reasoning about failures seems particularly challenging. +While not every network may allow for a polynomial-time analysis, +we see much potential in automata-theoretic approaches, +and we hope this article can inspire the community to conduct more research +in this area. + +We understand our approach as a first step and believe that it opens the door to +verify many other infinite state systems whose configurations +cannot explicitly be represented anymore. +For example, we have recently extended P-Rex to support a witness trace generation which +accounts for additional metrics, and for example selects (among a possibly infinite number of witness traces) +the ones that minimize the number of hops, latency, or the stack height that corresponds to the number +of MPLS tunnels. This is +achieved by extending the PDA reachability analysis with multi-dimensional weights. + +Another interesting avenue for future research is +the study of similar approaches for control plane verification +or for supporting capacity planning, also taking into account +resource constraints on failover paths. ## References From f3950b5605f5c3b03cbf1caa4568691804c39064 Mon Sep 17 00:00:00 2001 From: Thomas Fenz Date: Tue, 7 Jul 2020 20:06:51 +0200 Subject: [PATCH 06/12] minor changes; updated image --- _posts/2020-06-24-aalwines.md | 13 +++++++------ assets/images/aalwines-screenshot.png | Bin 1090348 -> 849497 bytes 2 files changed, 7 insertions(+), 6 deletions(-) diff --git a/_posts/2020-06-24-aalwines.md b/_posts/2020-06-24-aalwines.md index 11878b8..74ed298 100644 --- a/_posts/2020-06-24-aalwines.md +++ b/_posts/2020-06-24-aalwines.md @@ -1,6 +1,6 @@ --- layout: post -title: "Toward Polynomial-Time Verification of Networks with Infinite State Space: An Automata-Theoretic Approach" +title: "Toward Polynomial-Time Verification of Networks with Infinite State Spaces: An Automata-Theoretic Approach" subtitle: "The AalWiNes What-if Analysis Suite" authors: [schmid, srba] categories: [research, network, verification] @@ -18,7 +18,8 @@ While several interesting automated approaches to verify and operate networks are emerging, offering an attractive alternative to today’s pragmatic and manual “fix it when it breaks” approach, existing solutions often only provide a limited and inefficient support for reasoning about failure -scenarios. In particular, verifying networks is a complex task, even for computers. For example, many existing automated solutions require to test each possible failure scenario (respectively, each possible dataplane) individually, resulting in a runtime which can be exponential in the number of failures, k; which makes this approach impractical for large-scale communication networks. In fact, certain communication networks, such as networks based on MultiPath Label Switching (MPLS) or Segment Routing (SR), may even have a theoretically infinite configuration space: in MPLS and SR networks, default routes as well as failover routes depend on the label stack in the packet header, which may grow and shrink arbitrarily along the route. +scenarios. In particular, verifying networks is a complex task, even for computers. For example, many existing automated +solutions require to test each possible failure scenario (respectively, each possible dataplane) individually, resulting in a runtime which can be exponential in the number of failures; which makes this approach impractical for large-scale communication networks. In fact, certain communication networks, such as networks based on MultiPath Label Switching (MPLS) or Segment Routing (SR), may even have a theoretically infinite configuration space: in MPLS and SR networks, default routes as well as failover routes depend on the label stack in the packet header, which may grow and shrink arbitrarily along the route. In this article, we argue that automata-theoretic approaches can offer an interesting solution to these problems, allowing to perform fast verification, accounting even for failure scenarios and dealing with potentially infinite state spaces. @@ -32,7 +33,7 @@ failover tables) has the advantage that it also accounts for possible external changes, e.g., manual changes through the CLI, bugs, or changes made by -additional prototcols. Moreover, dataplane-based approaches can also reveal +additional protocols. Moreover, dataplane-based approaches can also reveal problems in the network operation introduced by the algorithms that generate the routing tables from the control plane specifications. @@ -95,14 +96,14 @@ Here is a quick intro to our tool: [![AalWiNes Quick Intro](http://img.youtube.com/vi/mvXAn9i7_Q0/0.jpg)](http://www.youtube.com/watch?v=mvXAn9i7_Q0 "AalWiNes Quick Intro") -P-Rex also allows to account for more complex traffic engineering aspects, such as load-balancing, +AalWiNes also allows to account for more complex traffic engineering aspects, such as load-balancing, by supporting nondeterminism, as well as more complex multi-operation chains. The tool includes several optimizations to further improve the performance, such as “top of stack reduction”, which safely calculates which labels can be at the top of stack in a given state of the PDA: the top of stack reduction technique greatly reduces the amount of transitions in the PDA. -We refer to our [tool website](https://whatif-tools.net/) as well as to our +We refer to our [tool website](https://aalwines.cs.aau.dk/) as well as to our [project website](https://github.com/DEIS-Tools/AalWiNes-Web). ## Conclusion and future work @@ -117,7 +118,7 @@ in this area. We understand our approach as a first step and believe that it opens the door to verify many other infinite state systems whose configurations cannot explicitly be represented anymore. -For example, we have recently extended P-Rex to support a witness trace generation which +For example, we have recently extended AalWiNes to support a witness trace generation which accounts for additional metrics, and for example selects (among a possibly infinite number of witness traces) the ones that minimize the number of hops, latency, or the stack height that corresponds to the number of MPLS tunnels. 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zm`Voiv5?a@W1xIwEcEcE{f1|0OU0Go{0rMhPIi1BVcRuY&*exUI)KV19LfAsbg-W) zI<{IJ^Cr?sL$-nLI(Dk?@z3v@f4|^Aetux|g(+s?>egj>9H#7k- zuR>2cb@Ci>eQD#S(bfw}=OykJxD)py`V2eOMhqCr=PKfD>IY;B=t$>v7Ir99k-ife z3Ao*P!xORrK%#Za=vfZ1jA*fA!bR_$B@`8ig2*O1SFESYxAl`cmyHju%WiLHdIF+n zYa!@cXk5O$$k(dW06lZ|0W!x~_tx3GdrR@5)^ARpWXyUP__j-9O}pBEK%L?{o9>Zg z1keIT=S>ld`l*fI6xzh(2|~z6`9*C2Gv6g9oO*IOfL%hFO<0~#y^Q>r=iJTZ*IXmPHw?RPi_&)d-EDA z9D<9b(KUAs8lrUu9EGQ z0oUsn>-^}!JUi@)nEjDdsVjh1eEk%gvL7Du0N3X{_04bCbapkOXDIC^G&AUB!!G0X zHUOwrf#~++1=g&kkHEqeUGqvEg#bzSY+8nR-3N&wPsOKz1Vv zQCV%1F^Prl`)QW325ZXPMja6W2Nt{U3N#X}C=K2E+7bqTlT`nfI@|?3{`FgRN+C#? z$As-43l?^L>c7Jq%RYc~Vm8(+@PGHm|9DR>jMBPof=&F~pJdNz1OT{5iY+UZS}`b2d^k14q`|3#gP1m zyQXw+aQ=6Xrri7A)c>ERo;;kx%D8XezAK03hWj{9KAex(xBmduq2nBK&;R>_cii(} zFW1s9d+-1LKX>1GcI43PFxgP^mp`@pKkRzSe}479$L$&ae~irk2J^oQ@_$R^?^eiv ftm*%kr6N~ Date: Tue, 7 Jul 2020 20:31:23 +0200 Subject: [PATCH 07/12] removed P-Rex reference --- _posts/2020-06-24-aalwines.md | 6 +----- 1 file changed, 1 insertion(+), 5 deletions(-) diff --git a/_posts/2020-06-24-aalwines.md b/_posts/2020-06-24-aalwines.md index 74ed298..aa960c9 100644 --- a/_posts/2020-06-24-aalwines.md +++ b/_posts/2020-06-24-aalwines.md @@ -89,7 +89,7 @@ The configurations are then put into a standardized, intermediate format which i The user can then define a query as described above, which leads the tool to prompt with a result (e.g. a trace). AalWiNes is a joint work at Aalborg University and the University of Vienna. -For MPLS specifically, we have developed the P-Rex tool [[1]](#references), recently reimplemented in C++. +For MPLS specifically, we have developed the AalWiNes tool, implemented in C++. The tool allows to verify a wide range of important network properties in polynomial time, parameterized by the $k$. Here is a quick intro to our tool: @@ -128,7 +128,3 @@ Another interesting avenue for future research is the study of similar approaches for control plane verification or for supporting capacity planning, also taking into account resource constraints on failover paths. - -## References - -\[1\] : P-Rex: Fast Verification of MPLS Networks with Multiple Link Failures. Jesper Stenbjerg Jensen, Troels Beck Krogh, Jonas Sand Madsen, Stefan Schmid, Jiri Srba, and Marc Tom Thorgersen. 14th ACM International Conference on emerging Networking EXperiments and Technologies (CoNEXT), Heraklion/Crete, Greece, December 2018. \ No newline at end of file From 6d7e116de46c27a4dcb43f076177e82f294c30fc Mon Sep 17 00:00:00 2001 From: Thomas Fenz Date: Wed, 8 Jul 2020 15:18:13 +0200 Subject: [PATCH 08/12] changed links, added reference --- _posts/2020-06-24-aalwines.md | 19 ++++++++++++++----- 1 file changed, 14 insertions(+), 5 deletions(-) diff --git a/_posts/2020-06-24-aalwines.md b/_posts/2020-06-24-aalwines.md index aa960c9..5747e1d 100644 --- a/_posts/2020-06-24-aalwines.md +++ b/_posts/2020-06-24-aalwines.md @@ -89,22 +89,24 @@ The configurations are then put into a standardized, intermediate format which i The user can then define a query as described above, which leads the tool to prompt with a result (e.g. a trace). AalWiNes is a joint work at Aalborg University and the University of Vienna. -For MPLS specifically, we have developed the AalWiNes tool, implemented in C++. +For MPLS specifically, we have devloped the AalWiNes tool suite, implemented in C++, and improving upon an earlier +prototype implementation in Python [[1]](#references). The tool allows to verify a wide range of important network properties in polynomial time, parameterized by the $k$. -Here is a quick intro to our tool: + +Here is a quick intro to AalWines, using an interative +web-browser integration of our tool available at [demo.aalwines.cs.aau.dk](https://demo.aalwines.cs.aau.dk/): [![AalWiNes Quick Intro](http://img.youtube.com/vi/mvXAn9i7_Q0/0.jpg)](http://www.youtube.com/watch?v=mvXAn9i7_Q0 "AalWiNes Quick Intro") AalWiNes also allows to account for more complex traffic engineering aspects, such as load-balancing, -by supporting nondeterminism, as well as -more complex multi-operation chains. +by supporting nondeterminism, as well as more complex multi-operation chains. The tool includes several optimizations to further improve the performance, such as “top of stack reduction”, which safely calculates which labels can be at the top of stack in a given state of the PDA: the top of stack reduction technique greatly reduces the amount of transitions in the PDA. We refer to our [tool website](https://aalwines.cs.aau.dk/) as well as to our -[project website](https://github.com/DEIS-Tools/AalWiNes-Web). +[project website](https://github.com/DEIS-Tools/AalWiNes). ## Conclusion and future work @@ -128,3 +130,10 @@ Another interesting avenue for future research is the study of similar approaches for control plane verification or for supporting capacity planning, also taking into account resource constraints on failover paths. + +## References + +\[1\] : P-Rex: Fast Verification of MPLS Networks with Multiple Link Failures. +Jesper Stenbjerg Jensen, Troels Beck Krogh, Jonas Sand Madsen, Stefan Schmid, Jiri Srba, +and Marc Tom Thorgersen. 14th ACM International Conference on emerging Networking EXperiments +and Technologies (CoNEXT), Heraklion/Crete, Greece, December 2018. \ No newline at end of file From 4156e89fe399841470a598b5ced4ee1148c096fa Mon Sep 17 00:00:00 2001 From: Thomas Fenz Date: Wed, 8 Jul 2020 15:46:14 +0200 Subject: [PATCH 09/12] updated article date + minor change in conclusio --- _posts/{2020-06-24-aalwines.md => 2020-07-08-aalwines.md} | 3 +-- 1 file changed, 1 insertion(+), 2 deletions(-) rename _posts/{2020-06-24-aalwines.md => 2020-07-08-aalwines.md} (98%) diff --git a/_posts/2020-06-24-aalwines.md b/_posts/2020-07-08-aalwines.md similarity index 98% rename from _posts/2020-06-24-aalwines.md rename to _posts/2020-07-08-aalwines.md index 5747e1d..be26e0d 100644 --- a/_posts/2020-06-24-aalwines.md +++ b/_posts/2020-07-08-aalwines.md @@ -109,8 +109,7 @@ We refer to our [tool website](https://aalwines.cs.aau.dk/) as well as to our [project website](https://github.com/DEIS-Tools/AalWiNes). ## Conclusion and future work - -We consider providing a low runtime critical for the success of network verification, +We consider providing a low runtime that is critical for the success of network verification, and reasoning about failures seems particularly challenging. While not every network may allow for a polynomial-time analysis, we see much potential in automata-theoretic approaches, From a320609eb5aa50832df9ba29ace418fd6f4b835a Mon Sep 17 00:00:00 2001 From: Thomas Fenz Date: Thu, 9 Jul 2020 14:42:55 +0200 Subject: [PATCH 10/12] minor changes --- _posts/2020-06-24-aalwines.md | 14 +++++++------- 1 file changed, 7 insertions(+), 7 deletions(-) diff --git a/_posts/2020-06-24-aalwines.md b/_posts/2020-06-24-aalwines.md index aa960c9..4d6d314 100644 --- a/_posts/2020-06-24-aalwines.md +++ b/_posts/2020-06-24-aalwines.md @@ -40,7 +40,7 @@ that generate the routing tables from the control plane specifications. Let us consider the verification of forwarding rules in MPLS routing tables as an example. In a nutshell, in MPLS, packet labels can be nested in order to provide tunneling through the network or to handle link -failures by fast-reroute mechanism. This mechanism relies on pushing a new MPLS +failures by the fast-reroute mechanism. The mechanism relies on pushing a new MPLS label on top of the label stack, to redirect the flow to go around the failed link. This mechanism can be applied several times in case of multiple link failures, creating larger and larger (in theory: unbounded) @@ -73,8 +73,8 @@ the regular expressions for the initial header and the final header of the query can each be converted to first a Nondeterministic Finite Automaton (NFA) and then to a Pushdown Automaton (PDA). The path query is converted to an NFA, which can then be used to restrict (by synchronous product) -the behaviour of the PDA constructed based on the network model. -The three PDAs can be combined into a single PDA that we can give +the behavior of the PDA constructed based on the network model. +The three PDAs can be combined into a single PDA that can be given to the backend engine that checks the emptiness of the PDA language. In case the language is nonempty, we can return a witness trace to demonstrate the reason why the query is satisfied. All these operations can be performed in polynomial time, @@ -85,7 +85,7 @@ leveraging a classic result by J. Büchi. As a case study and to explore the feasibility of such an automata-theoretic approach, we developed a framework, the AalWiNes suite, which allows to load an arbitrary network topology (e.g., from the topology zoo dataset) as well as a set of router configurations (e.g., from Juniper routers). -The configurations are then put into a standardized, intermediate format which is vendor independent. +The configurations are put into a standardized, intermediate format which is vendor independent. The user can then define a query as described above, which leads the tool to prompt with a result (e.g. a trace). AalWiNes is a joint work at Aalborg University and the University of Vienna. @@ -108,8 +108,8 @@ We refer to our [tool website](https://aalwines.cs.aau.dk/) as well as to our ## Conclusion and future work -We consider providing a low runtime critical for the success of network verification, -and reasoning about failures seems particularly challenging. +Our aim is to provide a low runtime which is critical for the success of network +verification, however, reasoning about failures seems particularly challenging with respect to the computational complexity. While not every network may allow for a polynomial-time analysis, we see much potential in automata-theoretic approaches, and we hope this article can inspire the community to conduct more research @@ -119,7 +119,7 @@ We understand our approach as a first step and believe that it opens the door to verify many other infinite state systems whose configurations cannot explicitly be represented anymore. For example, we have recently extended AalWiNes to support a witness trace generation which -accounts for additional metrics, and for example selects (among a possibly infinite number of witness traces) +accounts for additional metrics; for example, the tool can now select (among a possibly infinite number of witness traces) the ones that minimize the number of hops, latency, or the stack height that corresponds to the number of MPLS tunnels. This is achieved by extending the PDA reachability analysis with multi-dimensional weights. From fcbaa99f9836bda4b2809cfc9031735bf501aa30 Mon Sep 17 00:00:00 2001 From: Thomas Fenz Date: Thu, 9 Jul 2020 15:08:04 +0200 Subject: [PATCH 11/12] minor change --- _posts/2020-07-08-aalwines.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/_posts/2020-07-08-aalwines.md b/_posts/2020-07-08-aalwines.md index 7dc23a9..665e6b2 100644 --- a/_posts/2020-07-08-aalwines.md +++ b/_posts/2020-07-08-aalwines.md @@ -40,9 +40,9 @@ that generate the routing tables from the control plane specifications. Let us consider the verification of forwarding rules in MPLS routing tables as an example. In a nutshell, in MPLS, packet labels can be nested in order to provide tunneling through the network or to handle link -failures by the fast-reroute mechanism. The mechanism relies on pushing a new MPLS +failures by the fast-reroute mechanism. This mechanism relies on pushing a new MPLS label on top of the label stack, to redirect the flow -to go around the failed link. This mechanism can be applied several times +to go around the failed link. The mechanism can be applied several times in case of multiple link failures, creating larger and larger (in theory: unbounded) numbers of MPLS labels on the label-stack. From e9f30a85871a61215c52c768a1f5e76303c84c89 Mon Sep 17 00:00:00 2001 From: Thomas Fenz Date: Thu, 9 Jul 2020 15:11:26 +0200 Subject: [PATCH 12/12] updated article date --- _posts/{2020-07-08-aalwines.md => 2020-07-09-aalwines.md} | 0 1 file changed, 0 insertions(+), 0 deletions(-) rename _posts/{2020-07-08-aalwines.md => 2020-07-09-aalwines.md} (100%) diff --git a/_posts/2020-07-08-aalwines.md b/_posts/2020-07-09-aalwines.md similarity index 100% rename from _posts/2020-07-08-aalwines.md rename to _posts/2020-07-09-aalwines.md

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