Incremental, Inductive Coverability

We give an incremental, inductive (IC3) procedure to check coverability of well-structured transition systems. Our procedure generalizes the IC3 procedure for safety verification that has been successfully applied in finite-state hardware verification to infinite-state well-structured transition systems. We show that our procedure is sound, complete, and terminating for downward-finite well-structured transition systems---where each state has a finite number of states below it---a class that contains extensions of Petri nets, broadcast protocols, and lossy channel systems. We have implemented our algorithm for checking coverability of Petri nets. We describe how the algorithm can be efficiently implemented without the use of SMT solvers. Our experiments on standard Petri net benchmarks show that IC3 is competitive with state-of-the-art implementations for coverability based on symbolic backward analysis or expand-enlarge-and-check algorithms both in time taken and space usage.Comment: Non-reviewed version, original version submitted to CAV 2013; this is a revised version, containing more experimental results and some correction

Approaching the Coverability Problem Continuously

The coverability problem for Petri nets plays a central role in the verification of concurrent shared-memory programs. However, its high EXPSPACE-complete complexity poses a challenge when encountered in real-world instances. In this paper, we develop a new approach to this problem which is primarily based on applying forward coverability in continuous Petri nets as a pruning criterion inside a backward coverability framework. A cornerstone of our approach is the efficient encoding of a recently developed polynomial-time algorithm for reachability in continuous Petri nets into SMT. We demonstrate the effectiveness of our approach on standard benchmarks from the literature, which shows that our approach decides significantly more instances than any existing tool and is in addition often much faster, in particular on large instances.Comment: 18 pages, 4 figure

Incremental Inductive Coverability for Alternating Finite Automata

V tejto práci navrhujeme špecializáciu algoritmu inductive incremental  coverability, ktorá rieši problém prázdnosti alternujúcich konečných automatov. Experimentujeme s rôznymi návrhovými rozhodnutiami, analyzujeme ich a dokazujeme ich korektnosť. Aj keď je známe, že problém je sám o sebe PSpace-ťažký, zameriavame sa na to, aby bolo rozhodovanie prázdnosti výpočetne prijateľné v niektorých triedach automatov s praktickým využitím. Dosiahli sme niekoľko zaujímavýcch výsledkov v porovnaní so špičkovými algoritmami, predovšetkým v porovnaní s algoritmami založenými na protireťazcoch.In this work, we propose a specialization of the inductive incremental coverability algorithm that solves alternating finite automata emptiness problem. We experiment with various design decisions, analyze them and prove their correctness. Even though the problem itself is PSpace-complete, we are focusing on making the decision of emptiness computationally feasible for some practical classes of applications. We have obtained interesting comparative results against state-of-the-art algorithms, especially in comparison with antichain-based algorithms.

Coverability Synthesis in Parametric Petri Nets

We study Parametric Petri Nets (PPNs), i.e., Petri nets for which some arc weights can be parameters. In that setting, we address a problem of parameter synthesis, which consists in computing the exact set of values for the parameters such that a given marking is coverable in the instantiated net. Since the emptiness of that solution set is already undecidable for general PPNs, we address a special case where parameters are used only as input weights (preT-PPNs), and consequently for which the solution set is downward-closed. To this end, we invoke a result for the representation of upward closed set from Valk and Jantzen. To use this procedure, we show we need to decide universal coverability, that is decide if some marking is coverable for every possible values of the parameters. We therefore provide a proof of its EXPSPACE-completeness, thus settling the previously open problem of its decidability. We also propose an adaptation of this reasoning to the case of parameters used only as output weights (postT-PPNs). In this case, the condition to use this procedure can be reduced to the decidability of the existential coverability, that is decide if there exists values of the parameters making a given marking coverable. This problem is known decidable but we provide here a cleaner proof, providing its EXPSPACE-completeness, by reduction to Omega Petri Nets

Coverability for Parallel Programs

Tato diplomová práce se zabývá automatickou verifikací systémů s paralelně běžícími procesy. Práce diskutuje existující metody a možnosti jejich optimalizace. Stávající techniky jsou založeny na hledání induktivního invariantu (například pomocí techniky zjemňování abstrakce řízené protipříklady (CEGAR)). Efektivnost metod závisí na velikosti nalezeného invariantu. V rámci této diplomové práce jsme nalezli možnost zlepšení metod díky zaměření se na hledání invariantů minimální velikosti. Naimplementovali jsme nástroj, který zajišťuje prohledávání prostoru invariantů systému. Naše experimentální výsledky ukazují, že mnoho existujících systémů užívaných v praxi má skutečně mnohem menší invarianty než ty, které lze nalézt stávajícími metodami. Závěry a výsledky této práce budou sloužit jako základ budoucího výzkumu, jehož cílem bude navržení optimální metody pro vypočítání malých invariantů paralelních systémů.This work is focusing on automatic verification of systems with parallel running processes. We discuss the existing methods and certain possibilities of optimizing them. Existing techniques are essentially based on finding an inductive invariant (for instance using a variant of counterexample-guided abstract refinement (CEGAR)). The effectiveness of these methods depends on the size of the invariant. In this thesis, we explored the possibility of improving the methods by focusing on finding invariants of minimal size. We implemented a tool that facilitates exploring the space of invariants of the system under scrutiny. Our experimental results show that many practical existing systems indeed have invariants that are much smaller than what can be found by the existing methods. The conjectures and the results of the work will serve as a basis of future research of an efficient method for finding small invariants of parallel systems.

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 23rd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2020, which took place in Dublin, Ireland, in April 2020, and was held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The 31 regular papers presented in this volume were carefully reviewed and selected from 98 submissions. The papers cover topics such as categorical models and logics; language theory, automata, and games; modal, spatial, and temporal logics; type theory and proof theory; concurrency theory and process calculi; rewriting theory; semantics of programming languages; program analysis, correctness, transformation, and verification; logics of programming; software specification and refinement; models of concurrent, reactive, stochastic, distributed, hybrid, and mobile systems; emerging models of computation; logical aspects of computational complexity; models of software security; and logical foundations of data bases.