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Symbolic algorithms for solving games of infinite duration.

Project description

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A package of symbolic algorithms using binary decision diagrams (BDDs) for synthesizing implementations from [temporal logic specifications][specs]. This is useful for designing systems, especially vehicles that carry humans.


  • [Synthesis][synthesis] algorithms for [Moore][moore] or [Mealy][mealy] implementations of:

    • [generalized Streett(1)][streett1] specifications (known as [GR(1)][gr1])
    • generalized Rabin(1) specifications ([counter-strategies][rabin1] to GR(1))
    • detection of trivial realizability in GR(1) specifications.


  • Enumeration of state machines (as networkx graphs) from the synthesized symbolic implementations. See

  • Facilities to simulate the resulting implementations with little and readable user code. See omega.steps.

  • Code generation for the synthesized symbolic implementations. This code is correct-by-construction.

  • [First-order][fol] [linear temporal logic][LTL] (LTL) with [rigid quantification][rigid quantification] and substitution. See omega.logic.lexyacc, omega.logic.ast, and omega.logic.syntax.

  • [Bitblaster][bitblasting] of quantified integer arithmetic (integers -> bits). See omega.logic.bitvector.

  • Translation from [past][past LTL] to future LTL, using [temporal testers][temporal testers]. See omega.logic.past.

  • Symbolic automata that manage first-order formulas by seamlessly using [binary decision diagrams][bdd] (BDDs) underneath. You can:

    • declare variables and constants
    • translate: 1. formulas to BDDs and 2. BDDs to minimal formulas via minimal covering
    • quantify
    • substitute
    • prime/unprime variables
    • get the support of predicates
    • pick satisfying assignments (or work with iterators)
    • define operators

    See omega.symbolic.temporal and omega.symbolic.fol for more details.

  • Facilities to write symbolic fixpoint algorithms. See omega.symbolic.fixpoint and

  • Conversion from graphs annotated with formulas to temporal logic formulas. These graphs can help specify transition relations. The translation is in the spirit of [predicate-action diagrams][tla-in-pictures].

    See omega.symbolic.logicizer and omega.automata for more details.

  • Enumeration and plotting of state predicates and actions represented as BDDs. See omega.symbolic.enumeration.


In [doc/][doc].


` pip install omega `


` python install `

The package and its dependencies are pure Python.

For solving demanding games, install the [Cython][cython] module dd.cudd that interfaces to [CUDD][cudd]. Instructions are available [at dd][dd].

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