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The MONA Project

MONA is a tool that translates formulas to finite-state automata. The formulas may express search patterns, temporal properties of reactive systems, parse tree constraints, etc. MONA analyses the automaton resulting from the compilation and prints out "valid" or a counter-example.

MONA implements decision procedures for the Weak Second-order Theory of One or Two successors (WS1S/WS2S). The theory of one successor, known as WS1S, is a fragment of arithmetic augmented with second-order quantification over finite sets of natural numbers. Its first-order terms denote just natural numbers. The theory has no addition, since that would make it undecidable, but it has a unary operation +1, known as the successor function. WS2S is a generalization to tree structures. Since the theories are monadic second-order logics, we call our tool MONA.

Latest release: version 1.4-18, February 8 2020 (ChangeLog)