Summary

ldlsat is a SAT solver for LDL_f, an extension of LTL.

For each input LDL_f formula, ldlsat first translates it to MSO, and then passes the generated (equivalent) MSO formula to the mona tool for solving its satisfiability.

Examples

Propositional

$ echo 'a & (a -> b) -> b' | ldlsat
valid
$ echo 'a & !a' | ldlsat
unsatisfiable

LTL / Modal

$ echo '[{true}*]a -> a' | ldlsat
valid
$ echo '[{true}](a -> b) -> [{true}]a -> [{true}]b' | ldlsat  ## distribution (K)
valid
$ echo '[{true}]a -> a' | ldlsat  ## reflexitivity (T)
satisfiable
$ echo 'a -> [{true}]<{true}>a' | ldlsat  ## symmetry (B)
satisfiable

Note

• [] and <> in LTL are equivalent with [{true}*] and <{true}*> in LDL, respectively.
• [] and <> in standard propositional modal logics correspond with [{true}] and <{true}> in LDL, respectively.

LDL_f

$ echo '<{a}*>a -> a' | ldlsat
valid
$ echo '<{a & !b}; {!a & b}>(a & last) -> [{a}*; {b}]last' | ldlsat
valid
$ echo '<{a}; {!b}>last & [{a}]b' | ldlsat
unsatisfiable

Note that formulas should conform to this grammar.

Installation on Docker

• run docker build -t ldltools/ldlsat . in the top directory

Installation on Debian/Ubuntu

Prerequisites

• ocaml (v4.05 or higher. tested with 4.07.0)
  run: apt-get install ocaml
  Alternatively, you can install a particular version of the compiler using opam
  run: opam switch 4.07.0 for example
• opam (ocaml package manager)
  run: apt-get install opam
• ocaml packages: ocamlfind, yojson, ppx_deriving, ppx_deriving_yojson
  for each of these packages,
  run: opam install package
• mona (v1.4)
  run: wget http://www.brics.dk/mona/download/mona-1.4-17.tar.gz
  expand the archive, and build/install the tool as is instructed.
• graphviz (optional)
  run: apt-get install graphviz

Build

• run make && make install in the top directory
  Tools including ldlsat will be built and installed into /usr/local/bin.
  To change the installation directory, run make PREFIX=<prefix> install instead (default: PREFIX=/usr/local).

Installation on macOS (Darwin)

In addition to the tools listed above, you also need the following:

• GNU common utilities
  run: brew install coreutils debianutils
• GNU sed/awk
  run: brew install gnu-sed gawk
• GNU make (v4.1 or higher)
  run: brew install remake
  and build with MAKE=remake remake instead of make

Testing

• run: make -C tests test
  run unit tests
• run: make -C tests dfa
  generate DFA files from various LDL_f formulas into tests/out