2011/06/15 by Velner, Yaron
#FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL) #Logic in Computer Science (cs.LO)
paper · doi:10.48550/arxiv.1106.3054
"Quantitative languages are 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. The class of mean-payoff automaton expressions, introduced in [1], is a class of quantitative languages, which is robust: it is closed under the four pointwise operations of max, min, sum and numerical complement."[1] In this paper we improve the computational complexity for solving the classical decision problems for mean-payoff automaton expressions: while the previously best known upper bound was 4EXPTIME, and no lower bound was known, we give an optimal PSPACE complete bound. As a consequence we also obtain a conceptually simple algorithm to solve the classical decision problems for mean-payoff automaton expressions.