Asynchronous Multi-Tape Automata Intersection: Undecidability and Approximation

TL;DR

This paper explores the computational properties of asynchronous multi-tape automata, revealing their undecidability in intersection problems and proposing an approximation algorithm with practical implementation.

Contribution

It introduces an under-approximation algorithm for intersection of asynchronous multi-tape automata and discusses conditions for exact intersection, supported by a prototype implementation.

Findings

Intersection of asynchronous multi-tape automata is not semi-decidable.

An algorithm for under-approximating automata intersection is developed.

Prototype implementation demonstrates practical effectiveness of the approach.

Abstract

When their reading heads are allowed to move completely asynchronously, finite-state automata with multiple tapes achieve a significant expressive power, but also lose useful closure properties---closure under intersection, in particular. This paper investigates to what extent it is still feasible to use multi-tape automata as recognizer of polyadic predicates on words. On the negative side, determining whether the intersection of asynchronous multi-tape automata is expressible is not even semidecidable. On the positive side, we present an algorithm that computes under-approximations of the intersection; and discuss simple conditions under which it can construct complete intersections. A prototype implementation and a few non-trivial examples demonstrate the algorithm in practice.