Paper Info
Title
On the Complexity of Equivalence and Minimisation for Q-weighted Automata
Abstract
This paper is concerned with the computational complexity of equivalence and minimisation for automata with transition weights in the ring Q of rational numbers. We use polynomial identity testing and the Isolation Lemma to obtain complexity bounds, focussing on the class NC of problems within P solvable in polylogarithmic parallel time. For finite Q-weighted automata, we give a randomised NC procedure that either outputs that two automata are equivalent or returns a word on which they differ. We also give an NC procedure for deciding whether a given automaton is minimal, as well as a randomised NC procedure that minimises an automaton. We consider probabilistic automata with rewards, similar to Markov Decision Processes. For these automata we consider two notions of equivalence: expectation equivalence and distribution equivalence. The former requires that two automata have the same expected reward on each input word, while the latter requires that each input word induce the same distribution on rewards in each automaton. For both notions we give algorithms for deciding equivalence by reduction to equivalence of Q-weighted automata. Finally we show that the equivalence problem for Q-weighted visibly pushdown automata is logspace equivalent to the polynomial identity testing problem.
Year
DOI
Venue
2013
10.2168/LMCS-9(1:08)2013
LOGICAL METHODS IN COMPUTER SCIENCE
Keywords
Field
DocType
weighted automata,equivalence checking,polynomial identity testing,minimisation
Quantum finite automata,Discrete mathematics,Automata theory,Combinatorics,Deterministic automaton,Continuous spatial automaton,Nested word,Timed automaton,DFA minimization,Mathematics,ω-automaton
Journal
Volume
Issue
ISSN
9
1
1860-5974
Citations 
PageRank 
References 
8
0.52
15
Authors
5
Name
Order
Citations
PageRank
Stefan Kiefer134536.87
Andrzej S. Murawski232432.93
Joël Ouaknine3148199.25
Björn Wachter432620.09
James Worrell5104081.17