Transformations of Logic Programs on Infinite Lists

TL;DR

This paper extends logic programming to infinite lists with -programs, providing transformation rules and a methodology for verifying properties of reactive systems and infinite sequences.

Contribution

It introduces -programs for infinite lists, along with correct transformation rules and a verification methodology for properties of reactive systems.

Findings

Transformation rules preserve perfect model semantics

Methodology effectively verifies properties of Buechi automata

Applicable to properties of -regular languages

Abstract

We consider an extension of logic programs, called \omega-programs, that can be used to define predicates over infinite lists. \omega-programs allow us to specify properties of the infinite behavior of reactive systems and, in general, properties of infinite sequences of events. The semantics of \omega-programs is an extension of the perfect model semantics. We present variants of the familiar unfold/fold rules which can be used for transforming \omega-programs. We show that these new rules are correct, that is, their application preserves the perfect model semantics. Then we outline a general methodology based on program transformation for verifying properties of \omega-programs. We demonstrate the power of our transformation-based verification methodology by proving some properties of Buechi automata and \omega-regular languages.