Symbolic Boolean manipulation with ordered binary-decision diagrams
ACM Computing Surveys (CSUR)
Finite automata, formal logic, and circuit complexity
Finite automata, formal logic, and circuit complexity
Languages, automata, and logic
Handbook of formal languages, vol. 3
The pointer assertion logic engine
Proceedings of the ACM SIGPLAN 2001 conference on Programming language design and implementation
Verification of a Sliding Window Protocol Using IOA and MONA
FORTE/PSTV 2000 Proceedings of the FIP TC6 WG6.1 Joint International Conference on Formal Description Techniques for Distributed Systems and Communication Protocols (FORTE XIII) and Protocol Specification, Testing and Verification (PSTV XX)
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
Bounded Model Construction for Monadic Second-Order Logics
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
Hardware Verification using Monadic Second-Order Logic
Proceedings of the 7th 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
Logical specification of regular relations for NLP
Natural Language Engineering
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BDDs and their algorithms implement a decision procedure for Quantified Propositional Logic. BDDs are a kind of acyclic automata. But unrestricted automata (recognizing unbounded strings of bit vectors) can be used to decide monadic second-order logics, which are more expressive. Prime examples are WS1S, a number-theoretic logic, or the string-based logical notation of introductory texts. One problem is that it is not clear which one is to be preferred in practice. For example, it is not known whether these two logics are computationally equivalent to within a linear factor, that is, whether a formula 驴 of one logic can be transformed to a formula %phis;驴 of the other such that %phis;驴 is true if and only if 驴 is and such that 驴驴 is decided in time linear in that of the time for 驴.Another problem is that first-order variables in either version are given automata-theoretic semantics according to relativizations, which are syntactic means of restricting the domain of quantification of a variable. Such relativizations lead to technical arbitrations that may involve normalizing each subformula in an asymmetric manner or may introduce spurious state space explosions.In this paper, we investigate these problems through studies of congruences on strings. This algebraic framework is adapted to language-theoretic relativizations, where regular languages are intersected with restrictions. The restrictions are also regular languages. We introduce ternary and sexpartite characterizations of relativized regular languages. From properties of the resulting congruences, we are able to carry out detailed state space analyses that allow us to address the two problems.We report briefly on practical experiments that support our results. We conclude that WS1S with first-order variables can be robustly implemented in a way that efficiently subsumes string-based notations.