Finite Automata with Time-Delay Blocks (Extended Version)

TL;DR

This paper introduces automata with delay blocks (ADBs), extending finite automata to include variable time delays, and analyzes their expressive power, closure properties, and decision problems in a discrete-time setting.

Contribution

The work defines ADBs, explores their language class, and studies their closure properties and computational complexity of key decision problems.

Findings

ADBs strictly include regular languages.

Decidability of emptiness and membership in polynomial time.

Model checking ADBs against regular languages is PSPACE-complete.

Abstract

The notion of delays arises naturally in many computational models, such as, in the design of circuits, control systems, and dataflow languages. In this work, we introduce \emph{automata with delay blocks} (ADBs), extending finite state automata with variable time delay blocks, for deferring individual transition output symbols, in a discrete-time setting. We show that the ADB languages strictly subsume the regular languages, and are incomparable in expressive power to the context-free languages. We show that ADBs are closed under union, concatenation and Kleene star, and under intersection with regular languages, but not closed under complementation and intersection with other ADB languages. We show that the emptiness and the membership problems are decidable in polynomial time for ADBs, whereas the universality problem is undecidable. Finally we consider the linear-time model checking problem, i.e., whether the language of an ADB is contained in a regular language, and show that the model checking problem is PSPACE-complete.