Extended Computation Tree Logic

TL;DR

This paper introduces an extended version of CTL with language-refined temporal operators, enhancing expressive power while maintaining polynomial-time model checking, thus promising for verification applications.

Contribution

It proposes a generic extension of CTL with language-based until operators, analyzing their complexity and expressive power compared to existing logics.

Findings

Polynomial-time model checking with context-free language extensions

Enhanced expressive power over standard CTL

Comparison with CTL* and PDL extensions

Abstract

We introduce a generic extension of the popular branching-time logic CTL which refines the temporal until and release operators with formal languages. For instance, a language may determine the moments along a path that an until property may be fulfilled. We consider several classes of languages leading to logics with different expressive power and complexity, whose importance is motivated by their use in model checking, synthesis, abstract interpretation, etc. We show that even with context-free languages on the until operator the logic still allows for polynomial time model-checking despite the significant increase in expressive power. This makes the logic a promising candidate for applications in verification. In addition, we analyse the complexity of satisfiability and compare the expressive power of these logics to CTL* and extensions of PDL.