Proceedings ArticleDOI
On simultaneously determinizing and complementing omega -automata
E.A. Emerson,C.S. Jutla +1 more
- pp 333-342
TLDR
The authors give a construction to determine and complement simultaneously a Buchi automaton in infinite strings, with an exponential blowup in states and a linear blow up in the number of pairs, which permits exponentially improved essentially optimal decision procedures for various modal logics of programs.Abstract:
The authors give a construction to determine and complement simultaneously a Buchi automaton in infinite strings, with an exponential blowup in states and a linear blowup in the number of pairs. An exponential lower bound is already known. The previous best construction was double exponential. The present result permits exponentially improved essentially optimal decision procedures for various modal logics of programs. It also gives exponentially improved conversions between various kinds of omega automata. >read more
Citations
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Book
Dynamic Logic
TL;DR: This book provides the first comprehensive introduction to Dynamic Logic, a system of remarkable unity that is theoretically rich as well as of practical value.
Book ChapterDOI
Automata on infinite objects
TL;DR: This chapter discusses the formulation of two interesting generalizations of Rabin's Tree Theorem and presents some remarks on the undecidable extensions of the monadic theory of the binary tree.
Proceedings ArticleDOI
Tree automata, mu-calculus and determinacy
E.A. Emerson,C.S. Jutla +1 more
TL;DR: It is shown that the propositional mu-calculus is equivalent in expressive power to finite automata on infinite trees, which provides a radically simplified, alternative proof of M.O. Rabin's (1989) complementation lemma for tree automata, which is the heart of one of the deepest decidability results.
Book ChapterDOI
An automata-theoretic approach to linear temporal logic
TL;DR: The automata-theoretic approach to linear temporal logic as discussed by the authors uses the theory of automata as a unifying paradigm for program specification, verification, and synthesis Both programs and specifications are in essence descriptions of computations These computations can be viewed as words over some alphabet.
Logics of Programs.
Dexter Kozen,Jerzy Tiuryn +1 more
TL;DR: In this paper, the authors present an introduction to some of the basic issues in the study of program logics and discuss their syntax, semantics, proof theory, and expressiveness.
References
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TL;DR: A propositional μ-calculus L μ is defined and study, which consists essentially of propositional modal logic with a least fixpoint operator that is syntactically simpler yet strictly more expressive than Propositional Dynamic Logic (PDL).
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On the synthesis of a reactive module
Amir Pnueli,Roni Rosner +1 more
TL;DR: An algorithm is presented based on a new procedure for checking the emptiness of Rabin automata on infinite trees in time exponential in the number of pairs, but only polynomial in theNumber of states, which leads to a synthesis algorithm whose complexity is doubleonential in the length of the given specification.
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On a Decision Method in Restricted Second Order Arithmetic
TL;DR: The interpreted formalism of SC as mentioned in this paper is a fraction of the restricted second order theory of natural numbers, or of the first-order theory of real numbers, and it is easy to see that SC is equivalent to the first order theory [Re, +, Pw, Nn], whereby Re, + are the sets of non-negative reals, integral powers of 2, and natural numbers.
Journal ArticleDOI
Propositional dynamic logic of regular programs
TL;DR: A formal syntax and semantics for the propositional dynamic logic of regular programs is defined and principal conclusions are that deciding satisfiability of length n formulas requires time d n /log n for some d > 1, and that satisfiability can be decided in nondeterministic time cn for some c.