Cut-elimination and the decidability of reachability in alternating pushdown systems

We propose a new approach to formalize alternating pushdown systems as natural-deduction style inference systems. In this approach, the decidability of reachability can be proved as a simple consequence of a cut-elimination theorem for the corresponding inference system. Then, we show how this result can be used to extend an alternating pushdown system into a complete system where, for every configuration $A$, either $A$ or $\neg A$ is provable. The key idea is that cut-elimination permits to build a system where a proposition of the form $\neg A$ has a co-inductive (hence possibly infinite) proof if and only if it has an inductive (hence finite) proof

Complementation: a bridge between finite and infinite proofs

When a proposition has no proof in an inference system, it is sometimes useful to build a counter-proof explaining, step by step, the reason of this non-provability. In general, this counter-proof is a (possibly) infinite co-inductive proof in a different inference system. In this paper, we show that, for some decidable inference systems, this (possibly) infinite proof has a representation as a finite proof in yet another system, equivalent to the previous one

A Completion Method to Decide Reachability in Rewrite Systems

International audienceThe Knuth-Bendix method takes in argument a finite set of equations and rewrite rules and, when it succeeds, returns an algorithm to decide if a term is equivalent to another modulo these equations and rules. In this paper, we design a similar method that takes in argument a finite set of rewrite rules and, when it succeeds, returns an algorithm to decide not equivalence but reachability modulo these rules, that is if a term reduces to another. As an application, we give new proofs of the decidability of reachability in finite ground rewrite systems and in pushdown systems

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 22nd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2019, which took place in Prague, Czech Republic, in April 2019, held as part of the European Joint Conference on Theory and Practice of Software, ETAPS 2019. The 29 papers presented in this volume were carefully reviewed and selected from 85 submissions. They deal with foundational research with a clear significance for software science

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 25th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2022, which was held during April 4-6, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 23 regular papers presented in this volume were carefully reviewed and selected from 77 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 25th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2022, which was held during April 4-6, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 23 regular papers presented in this volume were carefully reviewed and selected from 77 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems

Alternating Vector Addition Systems with States

International audienceAlternating vector addition systems are obtained by equipping vector addition systems with states (VASS) with 'fork' rules, and provide a natural setting for infinite-arena games played over a VASS. Initially introduced in the study of propositional linear logic, they have more recently gathered attention in the guise of multi-dimensional energy games for quantitative verification and synthesis. We show that establishing who is the winner in such a game with a state reachability objective is 2-ExpTime-complete. As a further application, we show that the same complexity result applies to the problem of whether a VASS is simulated by a finite-state system