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Linear B

Given a history of operations by a set of clients, and some singlethreaded model, attempts to show that the history is not linearizable with respect to that model. I am not certain the algorithm is correct yet; you should treat its results as plausible but verify by hand.

Named after the ruins where the Linear B script was discovered. You know, because we're testing if the history "be linear". YES IT'S A HISTORY PUN WORK WITH ME HERE OKAY?

Build Status


Via Clojars, as usual.


You can check a CAS register, initialized to nil, on an EDN history file, like so:

$ lein run data/cas-register/bad/bad-analysis.edn
data/cas-register/bad/bad-analysis.edn  false


Every logical transition in Knossos is represented by a pair of operations: an invoke, when the op begins, and a completion: either ok if the operation took place, fail if the operation did not take place, or info if you're not sure what happened, e.g. the operation timed out.

Operations are performed by logical processes, which can be any object. Typically you'll use small integers, e.g. 0, 1, 2, .... A process can only do one thing at a time. If a process times out after invoking an operation, it is said to be crashed and cannot perform another operation ever again.

Operations apply some transition function :f to the object they're interacting with, e.g. a :read or a :write. That function takes a :value, which encapsulates its arguments and return values. Values may be complex datatypes, so to represent a compare-and-set from 0 to 3, you might use :value [0 3].

So, a crashed write of 3, concurrent with a read of 3, might look like:

{:process 0, :type :invoke, :f :read, :value nil}
{:process 1, :type :invoke, :f :write, :value 3}
{:process 1, :type :info, :f :write, :value 3}
{:process 0, :type :ok, :f :read, :value 3}

If this is the entire history, we can infer that this history is linearizable: the crashed operation did in fact take place, and linearized prior to the read of 3. Notice that we don't have to provide a value for invocations if we don't know what it will be in advance--for instance, during a read. Knossos will fill in the invocation's :value from the completion operation, when possible.

You'll also need a model--see knossos.model, which defines a singlethreaded datatype and how it reacts to operations. Knossos defines some built-in models like a register, a register with compare-and-set, and a mutex, which you can choose at the CLI via --model mutex and so on.

At the command line

If you have a history for a compare-and-set register in an edn file, either as a series of operation maps, or as a single vector or list containing those operations, you can ask knossos to check it for you at the command line like so:

lein run --model cas-register my-file.edn

Knossos prints out the names of all files you asked it to check, followed by a tab, and then whether the history was valid. There are thre validity states:

  • true means the history was linearizable
  • false means the history was nonlinearizable
  • :unknown means knossos was unable to complete the analysis; e.g. it ran out of memory.

As a library

You'll probably want to invoke knossos as a library. Pull in knossos.model for a selection of models (or to write your own), and knossos.competition for the most efficient general-purpose algorithm, which runs both a graph search (knossos.linear) and a tree search (knossos.wgl) in parallel.

$ lein repl
knossos.cli=> (require '[knossos.model :as model] '[knossos.competition :as competition])
knossos.cli=> (competition/analysis (model/cas-register 0) [{:process 0, :type :invoke, :f :read, :value nil}
         #_=> {:process 1, :type :invoke, :f :write, :value 3}
                  #_=> {:process 1, :type :info, :f :write, :value 3}
                           #_=> {:process 0, :type :ok, :f :read, :value 3}])
{:configs ({:last-op {:f :read :index 3 :process 0 :type :ok :value 3}
            :model #knossos.model.CASRegister {:value 3}
                        :pending []})
 :valid? true}

Or we can try an invalid history. For instance, here's a minimal failing case adapted from a test on the RethinkDB key-value store, which allowed failed writes to be read by clients during pathological failure modes.

knossos.cli=> (def h (read-history "data/cas-register/bad/rethink-fail-minimal.edn"))

knossos.cli=> (pprint h)
[{:type :invoke, :f :write, :value 0, :process 0}
 {:type :ok, :f :write, :value 0, :process 0}
 {:type :invoke, :f :read, :value nil, :process 1}
 {:type :invoke, :f :write, :value 4, :process 2}
 {:type :ok, :f :read, :value 3, :process 1}
 {:type :ok, :f :write, :value 4, :process 2}
 {:type :invoke, :f :read, :value nil, :process 3}
 {:type :ok, :f :read, :value 4, :process 3}]

knossos.cli=> (def a (competition/analysis (model/cas-register) h))
{:configs ({:last-op {:f :write :index 1 :process 0 :type :ok :value 0}
            :model #knossos.model.CASRegister {:value 0}
            :pending [{:f :read :index 2 :process 1 :type :invoke :value 3}
                      {:f :write :index 3 :process 2 :type :invoke :value 4}]})
 :final-paths #{[{:model #knossos.model.CASRegister {:value 0}
                  :op {:f :write :index 1 :process 0 :type :ok :value 0}}
                 {:model #knossos.model.Inconsistent
                  {:msg "can't read 3 from register 0"}
                  :op {:f :read :index 4 :process 1 :type :ok :value 3}}]
                [{:model #knossos.model.CASRegister {:value 0}
                  :op {:f :write :index 1 :process 0 :type :ok :value 0}}
                 {:model #knossos.model.CASRegister {:value 4}
                  :op {:f :write :index 3 :process 2 :type :invoke :value 4}}
                 {:model #knossos.model.Inconsistent
                  {:msg "can't read 3 from register 4"}
                  :op {:f :read :index 4 :process 1 :type :ok :value 3}}]}
 :last-op {:f :write :index 1 :process 0 :type :ok :value 0}
 :op {:f :read :index 4 :process 1 :type :ok :value 3}
 :previous-ok {:f :write :index 1 :process 0 :type :ok :value 0}
 :valid? false}

:valid? false indicates the history was nonlinearizable. :op shows the first OK operation we weren't able to linearize through, and is a good hint as to where things in the history went wrong. We also have a :previous-ok which was the highest contiguously linearized OK operation in the history: where we knew things were still OK. In between those operations we have a series of :final-paths, which show various ways we could order the available concurrent operations at that time, and how each of those orders resulted in an illegal state transition, e.g. reading the value 3 from a register whose value was actually 4.

Visualization of faults

To visualize these errors, we can use to generate an interactive SVG visualization of the crucial part of the history.

knossos.cli=> (require '[ :as report])

knossos.cli=> (report/render-analysis! h a "linear.svg")

Now open linear.svg in your browser, and you can explore the different paths that lead to the checker running out of options.

Rendering of nonlinearizable result


Copyright © 2013, 2016, 2017 Kyle Kingsbury

Distributed under the Eclipse Public License, the same as Clojure.


Verifies the linearizability of experimentally accessible histories.






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