Two-way languages

The Regularity of Two-Way Nondeterministic Tree Automata Languages

We establish that regularly extended two-way nondeterministic tree automata with un-ranked alphabets have the same expressive power as regularly extended nondeterministic tree automata with unranked alphabets. We obtain this result by establishing regularly extended versions of a congruence on trees and of a congruence on, so called, views. Our motivation for the study of these tree models is t...

Determinizing Two-way Alternating Pebble Automata for Data Languages

We prove that for every integer k ≥ 1, two-way alternating kpebble automata and one-way deterministic k-pebble automata for data languages have the same recognition power.

Two-way Automata and Regular Languages of Overlapping Tiles

In this paper, we show how the study of two-way automata on words may relevantly be extended to the study of two-way automata on one-dimensional overlapping tiles that generalize finite words. Indeed, over tiles, languages recognizable by finite two-way automata (resp. multi-pebble automata) coincide with languages definable by Kleene’s (resp. Kleene’s extended) regular expressions. As an immed...

Unary Languages Recognized by Two-Way One-Counter Automata

A two-way deterministic finite state automaton with one counter (2D1CA) is a fundamental computational model that has been examined in many different aspects since sixties, but we know little about its power in the case of unary languages. Up to our knowledge, the only known unary nonregular languages recognized by 2D1CAs are those formed by strings having exponential length, where the exponent...

Characterizations of Bounded Semilinear Languages by One-Way and Two-way Deterministic Machines