On the Complexity of Equivalence and Minimisation for Q-weighted Automata
This paper is concerned with the computational complexity of equivalence and minimisation for automata with transition weights in the field 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 so...
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| Vydáno v: | Logical methods in computer science Ročník 9, Issue 1 |
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| Hlavní autoři: | , , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Logical Methods in Computer Science e.V
04.03.2013
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| Témata: | |
| ISSN: | 1860-5974, 1860-5974 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | This paper is concerned with the computational complexity of equivalence and
minimisation for automata with transition weights in the field 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. |
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| ISSN: | 1860-5974 1860-5974 |
| DOI: | 10.2168/LMCS-9(1:8)2013 |