Finite automata, formal logic, and circuit complexity
Finite automata, formal logic, and circuit complexity
Languages, automata, and logic
Handbook of formal languages, vol. 3
MOSEL: A FLexible Toolset for Monadic Second-Order Logic
TACAS '97 Proceedings of the Third International Workshop on Tools and Algorithms for Construction and Analysis of Systems
Mona: Monadic Second-Order Logic in Practice
TACAS '95 Proceedings of the First International Workshop on Tools and Algorithms for Construction and Analysis of Systems
MONA 1.x: New Techniques for WS1S and WS2S
CAV '98 Proceedings of the 10th International Conference on Computer Aided Verification
A Comparison of Presburger Engines for EFSM Reachability
CAV '98 Proceedings of the 10th International Conference on Computer Aided Verification
Hardware Verification using Monadic Second-Order Logic
Proceedings of the 7th International Conference on Computer Aided Verification
Symbolic Model Checking of Infinite State Systems Using Presburger Arithmetic
CAV '97 Proceedings of the 9th International Conference on Computer Aided Verification
Mona & Fido: The Logic-Automaton Connection in Practice
CSL '97 Selected Papers from the11th International Workshop on Computer Science Logic
Verified decision procedures for MSO on words based on derivatives of regular expressions
Proceedings of the 18th ACM SIGPLAN international conference on Functional programming
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BDDs and their algorithms implement a decision procedure for Quantified Propositional Logic. BDDs are a kind of acyclic automata. Unrestricted automata (recognizing unbounded strings of bit vectors) can be used to decide more expressive monadic second-order logics. Prime examples are WS1S, a number-theoretic logic, or a string-based notation such as those proposed in some introductory texts. It is not clear which one is to be preferred. Also, the inclusion of first-order variables in either version is problematic since their automata-theoretic semantics depends on restrictions. In this paper, we provide a mathematical framework to address these problems. We introduce three and six-valued characterizations of regular languages under restrictions. From properties of the resulting congruences, we are able to carry out detailed state space analyses that allows us to solve the two problems in WS1S in a way that require no extra normalization calculations compared to a naive decision procedure for string-oriented logic. We report briefly on the practical experiments that support our results. We conclude that WS1S with first-order variables is the superior choice among monadic second-order logics.