Weighted automata and weighted logics on infinite words

Quantitative aspects of systems like consumption of resources, output of goods, or reliability can be modeled by weighted automata. Recently, objectives like the average cost or the longtime peak power consumption of a system have been modeled by weighted automata which are not semiring weighted anymore. Instead, operations like limit superior, limit average, or discounting are used to determine the behavior of these automata. Here, we introduce a new class of weight structures subsuming a range of these models as well as semirings. Our main result shows that such weighted automata and Kleene-type regular expressions are expressively equivalent both for finite and infinite words.

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Weighted automata and weighted logics with discounting

Theoretical Computer Science ◽

10.1016/j.tcs.2009.03.029 ◽

2009 ◽

Vol 410 (37) ◽

pp. 3481-3494 ◽

Cited By ~ 22

Author(s):

Manfred Droste ◽

George Rahonis

Keyword(s):

Weighted Automata ◽

Weighted Logics

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Minimization of Limit-Average Automata

Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2021/388 ◽

2021 ◽

Author(s):

Jakub Michaliszyn ◽

Jan Otop

Keyword(s):

Polynomial Time ◽

Equivalence Relation ◽

Minimization Problem ◽

Value Function ◽

Equivalence Classes ◽

Minimization Algorithm ◽

Infinite Words ◽

Average Value ◽

Weighted Automata

LimAvg-automata are weighted automata over infinite words that aggregate weights along runs with the limit-average value function. In this paper, we study the minimization problem for (deterministic) LimAvg-automata. Our main contribution is an equivalence relation on words characterizing LimAvg-automata, i.e., the equivalence classes of this relation correspond to states of an equivalent LimAvg-automaton. In contrast to relations characterizing DFA, our relation depends not only on the function defined by the target automaton, but also on its structure. We show two applications of this relation. First, we present a minimization algorithm for LimAvg-automata, which returns a minimal LimAvg-automaton among those equivalent and structurally similar to the input one. Second, we present an extension of Angluin's L^*-algorithm with syntactic queries, which learns in polynomial time a LimAvg-automaton equivalent to the target one.

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