Decidability and syntactic control of interference

AbstractWe investigate the decidability of observational equivalence and approximation in Reynolds’ “Syntactic Control of Interference” (SCI), a prototypical functional-imperative language in which covert interference between functions and their arguments is prevented by the use of an affine typing discipline.By associating denotations of terms in a fully abstract “relational” model of finitary basic SCI (due to Reddy) with multitape finite state automata, we show that observational approximation is not decidable (even at first order), but that observational equivalence is decidable for all terms.We then consider the same problems for basic SCI extended with non-local control in the form of backwards jumps. We show that both observational approximation and observational equivalence are decidable in this “observably sequential” version of the language by describing a fully abstract games model in which strategies are regular languages

Beyond Language Equivalence on Visibly Pushdown Automata

We study (bi)simulation-like preorder/equivalence checking on the class of visibly pushdown automata and its natural subclasses visibly BPA (Basic Process Algebra) and visibly one-counter automata. We describe generic methods for proving complexity upper and lower bounds for a number of studied preorders and equivalences like simulation, completed simulation, ready simulation, 2-nested simulation preorders/equivalences and bisimulation equivalence. Our main results are that all the mentioned equivalences and preorders are EXPTIME-complete on visibly pushdown automata, PSPACE-complete on visibly one-counter automata and P-complete on visibly BPA. Our PSPACE lower bound for visibly one-counter automata improves also the previously known DP-hardness results for ordinary one-counter automata and one-counter nets. Finally, we study regularity checking problems for visibly pushdown automata and show that they can be decided in polynomial time.Comment: Final version of paper, accepted by LMC

Compositional software verification based on game semantics

One of the major challenges in computer science is to put programming on a firmer mathematical basis, in order to improve the correctness of computer programs. Automatic program verification is acknowledged to be a very hard problem, but current work is reaching the point where at least the foundational�· aspects of the problem can be addressed and it is becoming a part of industrial software development. This thesis presents a semantic framework for verifying safety properties of open sequ;ptial programs. The presentation is focused on an Algol-like programming language that embodies many of the core ingredients of imperative and functional languages and incorporates data abstraction in its syntax. Game semantics is used to obtain a compositional, incremental way of generating accurate models of programs. Model-checking is made possible by giving certain kinds of concrete automata-theoretic representations of the model. A data-abstraction refinement procedure is developed for model-checking safety properties of programs with infinite integer types. The procedure starts by model-checking the most abstract version of the program. If no counterexample, or a genuine one, is found, the procedure terminates. Otherwise, it uses a spurious counterexample to refine the abstraction for the next iteration. Abstraction refinement, assume-guarantee reasoning and the L* algorithm for learning regular languages are combined to yield a procedure for compositional verification. Construction of a global model is avoided using assume-guarantee reasoning and the L* algorithm, by learning assumptions for arbitrary subprograms. An implementation based on the FDR model checker for the CSP process algebra demonstrates practicality of the methods

Vector addition systems and their applications in the verification of computer programs

Vector Addition Systems (and, equivalently, Petri nets) are a widespread formalism for modelling across a spectrum of problem domains, from logistics to hardware simulation. In this thesis, we firstly explore two classic decidability problems for these models: reachability, whether one can get to a given configuration, and coverability, whether one can exceed it. These problems are sufficent to express a wide class of verification properties for models derived from real-world use cases, including safety and deadlock-freeness. We present and implement a number of approaches for solving both the coverability and reachability problems, including KReach, the first known implementation of a complete decider for the general Petri net reachability problem. Petri nets offer a natural model of concurrent processes and one of the most common modern use cases for the model is in the verification of safety properties for software, especially sofware with concurrency. In the later half of this work we address some approaches to deciding properties of programs written in Finitary Idealized Concurrent Algol (FICA), a prototypical language combining functional, imperative, and higher-order concurrent programming. We introduce a new family of “leafy” automata models, all based on a novel representation of internal configurations as a tree structure whose semantics is inspired by game-semantic interpretations of FICA terms. We give translations from such terms to our automata and across the work derive decidability of some useful properties for successively more expressive subsets of terms, using a variety of methods including via reachability on Petri nets. We believe these models will help to unify the game- and automata-theoretic views of programming languages and provide a useful basis on which to further study the theory of concurrency