We prove that the bisimulation-invariant fragment of weak monadic second-order logic (WMSO) is equivalent to the fragment of the modal μ-calculus where the application of the least fixpoint operator μp:ρ is restricted to formulas ρ that are continuous in p. Our proof is automata-theoretic in nature; in particular, we introduce a class of automata characterizing the expressive power of WMSO over tree models of arbitrary branching degree. The transition map of these automata is defined in terms of a logic FOE∞1 that is the extension of first-order logic with a generalized quantifier ε∞, where ε∞x:ρ means that there are infinitely many objects satisfying ρ. An important part of our work consists of a modeltheoretic analysis of FOE∞1. Copyright © 2014 ACM.
Carreiro F., Facchini A., Venema Y., Zanasi F. (2014). Weak MSO: Automata and expressiveness modulo bisimilarity. 1515 BROADWAY, NEW YORK, NY 10036-9998 USA : Association for Computing Machinery [10.1145/2603088.2603101].
Weak MSO: Automata and expressiveness modulo bisimilarity
Zanasi F.
2014
Abstract
We prove that the bisimulation-invariant fragment of weak monadic second-order logic (WMSO) is equivalent to the fragment of the modal μ-calculus where the application of the least fixpoint operator μp:ρ is restricted to formulas ρ that are continuous in p. Our proof is automata-theoretic in nature; in particular, we introduce a class of automata characterizing the expressive power of WMSO over tree models of arbitrary branching degree. The transition map of these automata is defined in terms of a logic FOE∞1 that is the extension of first-order logic with a generalized quantifier ε∞, where ε∞x:ρ means that there are infinitely many objects satisfying ρ. An important part of our work consists of a modeltheoretic analysis of FOE∞1. Copyright © 2014 ACM.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
