Silent Transitions in Automata with Storage

TL;DR

This paper investigates the conditions under which silent (lambda) transitions can be eliminated in automata with storage, using valence automata models with monoid-based storage mechanisms, and characterizes monoids allowing such transformations.

Contribution

It generalizes existing results on silent transitions by providing new characterizations for monoids that permit removal of lambda-transitions in automata with storage.

Findings

Characterizes monoids allowing lambda-transition removal for pushdown and counter storages.

Provides graph product-based classifications of monoids for silent transition elimination.

Extends known results to broader classes of storage mechanisms in automata.

Abstract

We consider the computational power of silent transitions in one-way automata with storage. Specifically, we ask which storage mechanisms admit a transformation of a given automaton into one that accepts the same language and reads at least one input symbol in each step. We study this question using the model of valence automata. Here, a finite automaton is equipped with a storage mechanism that is given by a monoid. This work presents generalizations of known results on silent transitions. For two classes of monoids, it provides characterizations of those monoids that allow the removal of \lambda-transitions. Both classes are defined by graph products of copies of the bicyclic monoid and the group of integers. The first class contains pushdown storages as well as the blind counters while the second class contains the blind and the partially blind counters.