## Schwentick, Thomas and Barthelmann, Klaus - Local Normal Forms for First-Order Logic with Applications to Games and Automata

dmtcs:254 - Discrete Mathematics & Theoretical Computer Science, January 1, 1999, Vol. 3 no. 3
Local Normal Forms for First-Order Logic with Applications to Games and Automata

Authors: Schwentick, Thomas and Barthelmann, Klaus

Building on work of Gaifman [Gai82] it is shown that every first-order formula is logically equivalent to a formula of the form ∃ x_1,...,x_l, \forall y, φ where φ is r-local around y, i.e. quantification in φ is restricted to elements of the universe of distance at most r from y. \par From this and related normal forms, variants of the Ehrenfeucht game for first-order and existential monadic second-order logic are developed that restrict the possible strategies for the spoiler, one of the two players. This makes proofs of the existence of a winning strategy for the duplicator, the other player, easier and can thus simplify inexpressibility proofs. \par As another application, automata models are defined that have, on arbitrary classes of relational structures, exactly the expressive power of first-order logic and existential monadic second-order logic, respectively.

Source : oai:HAL:hal-00958930v1
Volume: Vol. 3 no. 3
Published on: January 1, 1999
Submitted on: March 26, 2015
Keywords: First-order logic,existential monadic second-order logic,games,automata,locality,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]