On the organisation of program verification competitions

In this paper, we discuss the challenges that have to be addressed when organising program verification competitions. Our focus is on competitions for verification systems where the participants both formalise an informally stated requirement and (typically) provide some guidance for the tool to show it. The paper draws its insights from our experiences with organising a program verification competition at FoVeOOS 2011. We discuss in particular the following aspects: challenge selection, on-site versus online organisation, team composition and judging. We conclude with a list of recommendations for future competition organisers

Distributive groupoids are symmetric-by-medial: An elementary proof

summary:We present an elementary proof (purely in equational logic) that distributive groupoids are symmetric-by-medial

Automated verification of refinement laws

Demonic refinement algebras are variants of Kleene algebras. Introduced by von Wright as a light-weight variant of the refinement calculus, their intended semantics are positively disjunctive predicate transformers, and their calculus is entirely within first-order equational logic. So, for the first time, off-the-shelf automated theorem proving (ATP) becomes available for refinement proofs. We used ATP to verify a toolkit of basic refinement laws. Based on this toolkit, we then verified two classical complex refinement laws for action systems by ATP: a data refinement law and Back's atomicity refinement law. We also present a refinement law for infinite loops that has been discovered through automated analysis. Our proof experiments not only demonstrate that refinement can effectively be automated, they also compare eleven different ATP systems and suggest that program verification with variants of Kleene algebras yields interesting theorem proving benchmarks. Finally, we apply hypothesis learning techniques that seem indispensable for automating more complex proofs

ALICe: A Framework to Improve Affine Loop Invariant Computation

International audienceA crucial point in program analysis is the computation of loop invariants. Accurate invariants are required to prove properties on a program but they are difficult to compute. Extensive research has been carried out but, to the best of our knowledge, no benchmark has ever been developed to compare algorithms and tools. We present ALICe, a toolset to compare automatic computation techniques of affine loop scalar invariants. It comes with a benchmark that we built using 102 test cases which we found in the loop invariant bibliography, and interfaces with three analysis programs, that rely on different techniques: Aspic, ISL and PIPS. Conversion tools are provided to handle format heterogeneity of these programs. Experimental results show the importance of model coding and the poor performances of PIPS on concurrent loops. To tackle these issues, we use two model restructurations techniques whose correctness is proved in Coq, and discuss the improvements realized

Defining the meaning of TPTP formatted proofs

International audienceThe TPTP library is one of the leading problem libraries in the automated theorem proving community. Over time, support was added for problems beyond those in first-order clausal form. TPTP has also been augmented with support for various proof formats output by theorem provers. Such proofs can also be maintained in the TSTP proof library. In this paper we propose an extension of this framework to support the semantic specification of the inference rules used in proofs

Applying automated deduction to natural language understanding

AbstractVery few natural language understanding applications employ methods from automated deduction. This is mainly because (i) a high level of interdisciplinary knowledge is required, (ii) there is a huge gap between formal semantic theory and practical implementation, and (iii) statistical rather than symbolic approaches dominate the current trends in natural language processing. Moreover, abduction rather than deduction is generally viewed as a promising way to apply reasoning in natural language understanding. We describe three applications where we show how first-order theorem proving and finite model construction can efficiently be employed in language understanding.The first is a text understanding system building semantic representations of texts, developed in the late 1990s. Theorem provers are here used to signal inconsistent interpretations and to check whether new contributions to the discourse are informative or not. This application shows that it is feasible to use general-purpose theorem provers for first-order logic, and that it pays off to use a battery of different inference engines as in practice they complement each other in terms of performance.The second application is a spoken-dialogue interface to a mobile robot and an automated home. We use the first-order theorem prover spass for checking inconsistencies and newness of information, but the inference tasks are complemented with the finite model builder mace used in parallel to the prover. The model builder is used to check for satisfiability of the input; in addition, the produced finite and minimal models are used to determine the actions that the robot or automated house has to execute. When the semantic representation of the dialogue as well as the number of objects in the context are kept fairly small, response times are acceptable to human users.The third demonstration of successful use of first-order inference engines comes from the task of recognising entailment between two (short) texts. We run a robust parser producing semantic representations for both texts, and use the theorem prover vampire to check whether one text entails the other. For many examples it is hard to compute the appropriate background knowledge in order to produce a proof, and the model builders mace and paradox are used to estimate the likelihood of an entailment

Encodings of problems in effectively propositional logic

Solving various combinatorial problems by their translation to the propositional satisfiability problem has become commonly accepted. By optimising such translations and using efficient SAT solvers one can often solve hard problems in various domains, such as formal verification and planning