Logic underlies many fundamental techniques in computer science. It helps us to rigorously formalize these techniques and prove them correct. The last decade has witnessed a growing interest in the use of computational logic methods for program verification. It has attracted researchers from both computational logic and program verification communities, giving rise to a fruitful exchange of ideas and experiences.

It is well-known that the verification of partial correctness properties of imperative programs can be reduced to the satisfiability problem for constrained Horn clauses (CHCs). However, state-of-the-art solvers for constrained Horn clauses (or CHC solvers) based on predicate abstraction are sometimes unable to verify satisfiability because they look for models that are definable in a given class 𝓐 of constraints, called 𝓐-definable models. We introduce a transformation technique, called Predicate Pairing, which is able, in many interesting cases, to transform a set of clauses into an equisatisfiable set whose satisfiability can be proved by finding an 𝓐-definable model, and hence can be effectively verified by a state-of-the-art CHC solver. In particular, we prove that, under very general conditions on 𝓐, the unfold/fold transformation rules preserve the existence of an 𝓐-definable model, that is, if the original clauses have an 𝓐-definable model, then the transformed clauses have an 𝓐-definable model. The converse does not hold in general, and we provide suitable conditions under which the transformed clauses have an 𝓐-definable model if and only if the original ones have an 𝓐-definable model. Then, we present a strategy, called Predicate Pairing, which guides the application of the transformation rules with the objective of deriving a set of clauses whose satisfiability problem can be solved by looking for 𝓐-definable models. The Predicate Pairing (PP) strategy introduces a new predicate defined by the conjunction of two predicates occurring in the original set of clauses, together with a conjunction of constraints. We will show through some examples that an 𝓐-definable model may exist for the new predicate even if it does not exist for its defining atomic conjuncts. We will also present some case studies showing that Predicate Pairing plays a crucial role in the verification of relational properties of programs, that is, properties relating two programs (such as program equivalence) or two executions of the same program (such as non-interference). Finally, we perform an experimental evaluation of the proposed techniques to assess the effectiveness of Predicate Pairing in increasing the power of CHC solving.

Many applications require conformance with specifications that constrain the use of resources, such as execution time, energy, bandwidth, etc. We present a configurable framework for static resource usage verification where specifications can include data size-dependent resource usage functions, expressing both lower and upper bounds. Ensuring conformance with respect to such specifications is an undecidable problem. Therefore, to statically check such specifications, our framework infers the same type of resource usage functions, which safely approximate the actual resource usage of the program, and compares them against the specification. We review how this framework supports several languages and compilation output formats by translating them to an intermediate representation based on Horn clauses and using the configurability of the framework to describe the resource semantics of the input language. We provide a detailed formalization and extend the framework so that both resource usage specification and analysis/verification output can include preconditions expressing intervals for the input data sizes for which assertions are intended to hold, proved, or disproved. Most importantly, we also extend the classes of functions that can be checked. We also report on and provide results from an implementation within the Ciao/CiaoPP framework, as well as on a practical tool built by instantiating this framework for the verification of energy consumption specifications for imperative/embedded programs. Finally, we show as an example how embedded software developers can use this tool, in particular, for determining values for program parameters that ensure meeting a given energy budget while minimizing the loss in quality of service.

In this paper, we show how the notion of tree dimension can be used in the verification of constrained Horn clauses (CHCs). The dimension of a tree is a numerical measure of its branching complexity and the concept here applies to Horn clause derivation trees. Derivation trees of dimension zero correspond to derivations using linear CHCs, while trees of higher dimension arise from derivations using non-linear CHCs. We show how to instrument CHCs predicates with an extra argument for the dimension, allowing a CHC verifier to reason about bounds on the dimension of derivations. Given a set of CHCs P, we define a transformation of P yielding a dimension-bounded set of CHCs P≤k. The set of derivations for P≤k consists of the derivations for P that have dimension at most k. We also show how to construct a set of clauses denoted P>k whose derivations have dimension exceeding k. We then present algorithms using these constructions to decompose a CHC verification problem. One variation of this decomposition considers derivations of successively increasing dimension. The paper includes descriptions of implementations and experimental results.

A recent trend in object-oriented programming languages is the use of access permissions (APs) as an abstraction for controlling concurrent executions of programs. The use of AP source code annotations defines a protocol specifying how object references can access the mutable state of objects. Although the use of APs simplifies the task of writing concurrent code, an unsystematic use of them can lead to subtle problems. This paper presents a declarative interpretation of APs as linear concurrent constraint programs (lcc). We represent APs as constraints (i.e., formulas in logic) in an underlying constraint system whose entailment relation models the transformation rules of APs. Moreover, we use processes in lcc to model the dependencies imposed by APs, thus allowing the faithful representation of their flow in the program. We verify relevant properties about AP programs by taking advantage of the interpretation of lcc processes as formulas in Girard's intuitionistic linear logic (ILL). Properties include deadlock detection, program correctness (whether programs adhere to their AP specifications or not), and the ability of methods to run concurrently. By relying on a focusing discipline for ILL, we provide a complexity measure for proofs of the above-mentioned properties. The effectiveness of our verification techniques is demonstrated by implementing the Alcove tool that includes an animator and a verifier. The former executes the lcc model, observing the flow of APs, and quickly finding inconsistencies of the APs vis-à-vis the implementation. The latter is an automatic theorem prover based on ILL.