10.1007/978-3-642-15375-4_19
Chatterjee, Krishnendu
Krishnendu
Chatterjee0000-0002-4561-241X
Doyen, Laurent
Laurent
Doyen
Edelsbrunner, Herbert
Herbert
Edelsbrunner0000-0002-9823-6833
Henzinger, Thomas A
Thomas A
Henzinger0000−0002−2985−7724
Rannou, Philippe
Philippe
Rannou
Mean-payoff automaton expressions
LNCS
Schloss Dagstuhl - Leibniz-Zentrum für Informatik
2010
2018-12-11T12:05:31Z
2020-01-16T12:37:04Z
conference
https://research-explorer.app.ist.ac.at/record/3853
https://research-explorer.app.ist.ac.at/record/3853.json
233260 bytes
application/pdf
Quantitative languages are an extension of boolean languages that assign to each word a real number. Mean-payoff automata are finite automata with numerical weights on transitions that assign to each infinite path the long-run average of the transition weights. When the mode of branching of the automaton is deterministic, nondeterministic, or alternating, the corresponding class of quantitative languages is not robust as it is not closed under the pointwise operations of max, min, sum, and numerical complement. Nondeterministic and alternating mean-payoff automata are not decidable either, as the quantitative generalization of the problems of universality and language inclusion is undecidable. We introduce a new class of quantitative languages, defined by mean-payoff automaton expressions, which is robust and decidable: it is closed under the four pointwise operations, and we show that all decision problems are decidable for this class. Mean-payoff automaton expressions subsume deterministic meanpayoff automata, and we show that they have expressive power incomparable to nondeterministic and alternating mean-payoff automata. We also present for the first time an algorithm to compute distance between two quantitative languages, and in our case the quantitative languages are given as mean-payoff automaton expressions.