2 research outputs found
Decidable Weighted Expressions with Presburger Combinators
In this paper, we investigate the expressive power and the algorithmic
properties of weighted expressions, which define functions from finite words to
integers. First, we consider a slight extension of an expression formalism,
introduced by Chatterjee. et. al. in the context of infinite words, by which to
combine values given by unambiguous (max,+)-automata, using Presburger
arithmetic. We show that important decision problems such as emptiness,
universality and comparison are PSpace-c for these expressions. We then
investigate the extension of these expressions with Kleene star. This allows to
iterate an expression over smaller fragments of the input word, and to combine
the results by taking their iterated sum. The decision problems turn out to be
undecidable, but we introduce the decidable and still expressive class of
synchronised expressions.Comment: FCT2017 Acceptanc