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Logical specifications of infinite computations

  • Wolfgang Thomas
  • Helmut Lescow
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 803)

Abstract

Starting from an identification of infinite computations with ω-words, we present a framework in which different classification schemes for specifications are naturally compared. Thereby we connect logical formalisms with hierarchies of descriptive set theory (e.g., the Borel hierarchy), of recursion theory, and with the hierarchy of acceptance conditions of ω-automata. In particular, it is shown in which sense these hierarchies can be viewed as classifications of logical formulas by the complexity measure of quantifier alternation. In this context, the automaton theoretic approach to logical specifications over ω-words turns out to be a technique to reduce quantifier complexity of formulas. Finally, we indicate some perspectives of this approach, discuss variants of the logical framework (first-order logic, temporal logic), and outline the effects which arise when branching computations are considered (i.e., when infinite trees instead of ω-words are taken as model of computation).

Keywords

Infinite words ω-languages descriptive set theory Cantor space Borel hierarchy recursion theory Büchi automata acceptance conditions regular ω-languages monadic second-order logic infinite games temporal logic infinite trees 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Wolfgang Thomas
    • 1
  • Helmut Lescow
    • 1
  1. 1.Institut für Informatik und Praktische MathematikChristian-Albrechts-Universität KielKiel

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