Tropical Two-Way Automata

Abstract

Part 2: Track B: Logic, Semantics, Specification and VerificationInternational audienceIn this paper we study two-way min-plus automata. We prove that two-way distance automata are equivalent to one-way distance automata. In the second part of the paper we show that, with general min-plus semirings, it is decidable whether every accepted word has a finite weight and that, in contrast, it is undecidable whether there exists a word accepted with a finite weight

Two-way representations and weighted automata

“…The study of two-way automata and representions in semirings that are not rationally additive requires further investigation. Specific cases have already been studied: Z in [1], or (Z ∪ {∞}, min, +) in [6].…”

Input- or output-unary sweeping transducers are weaker than their 2-way counterparts

“…This proves that sweeping transducers are weaker than general 2-way transducers. A recent paper shows that two-way N -automata on the tropical semiring N = ⟨(N ∪ {∞}), min, +⟩ are always equivalent to one-way automata, [5]. It is worthwhile observing that the tropical semiring is isomorphic to a sub-semiring of Rat (a * ) in the mapping n ↦ a n a * and that consequently an N -automaton is a particular case of a two-way transducer whose images have all ultimate period equal to 1.…”