On the Complexity of Parity Word Automata
Valerie King,Orna Kupferman,Moshe Y. Vardi +2 more
- pp 276-286
TLDR
It is shown that the special structure of the acceptance condition of parity automata can be used in order to solve the nonemptiness problem directly, with a dynamic graph algorithm of complexity O((n + m) log k).Abstract:
Different types of nondeterministic automata on infinite words differ in their succinctness and in the complexity for their nonemptiness problem. A simple translation of a parity automaton to an equivalent Buchi automaton is quadratic: a parity automaton with n states, m transitions, and index k may result in a Buchi automaton of size O((n + m)k). The best known algorithm for the nonemptiness problem of parity automata goes through Buchi automata, leading to a complexity of O((n + m)k). In this paper we show that while the translation of parity automata to Buchi automata cannot be improved, the special structure of the acceptance condition of parity automata can be used in order to solve the nonemptiness problem directly, with a dynamic graph algorithm of complexity O((n + m) log k).read more
Citations
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Book ChapterDOI
Better Quality in Synthesis through Quantitative Objectives
TL;DR: In this paper, the synthesis of optimal implementations requires the solution of lexicographic mean-payoff games (for safety requirements), and games with both lexicoographic mean payoff and parity objectives (for liveness requirements).
Posted Content
Better Quality in Synthesis through Quantitative Objectives
TL;DR: It is shown how automata with lexicographic mean-payoff conditions can be used to express many interesting quantitative properties for reactive systems, and how quantitative properties to measure the "goodness" of an implementation are used.
Proceedings ArticleDOI
Quantitative stochastic parity games
TL;DR: The existence of optimal pure memoryless strategies together with the polynomial-time solution for the one-player case implies that the quantitative two-player stochastic parity game problem is in NP ∩ co-NP, which generalizes a result of Condon for Stochastic games with reachability objectives.
Journal ArticleDOI
A Deterministic Subexponential Algorithm for Solving Parity Games
TL;DR: This work uses a completely different, and elementary, approach to obtain a deterministic subexponential algorithm for the solution of parity games, and is almost as fast as the randomized algorithms mentioned above.
Proceedings ArticleDOI
A deterministic subexponential algorithm for solving parity games
TL;DR: This work uses a completely different, and elementary, approach to obtain a deterministic subexponential algorithm for the solution of parity games, and is almost as fast as the randomized algorithms mentioned above.
References
More filters
Journal ArticleDOI
Depth-First Search and Linear Graph Algorithms
TL;DR: The value of depth-first search or “backtracking” as a technique for solving problems is illustrated by two examples of an improved version of an algorithm for finding the strongly connected components of a directed graph.
Journal ArticleDOI
Automatic verification of finite-state concurrent systems using temporal logic specifications
TL;DR: It is argued that this technique can provide a practical alternative to manual proof construction or use of a mechanical theorem prover for verifying many finite-state concurrent systems.
Journal ArticleDOI
Results on the propositional μ-calculus
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).
Book ChapterDOI
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.