Related papers: Tree dimension in verification of constrained Horn…

In this paper we investigate the use of the concept of tree dimension in Horn clause analysis and verification. The dimension of a tree is a measure of its non-linearity - for example a list of any length has dimension zero while a complete…

Developing an efficient non-linear Horn clause solver is a challenging task since the solver has to reason about the tree structures rather than the linear ones as in a linear solver. In this paper we propose an incremental approach to…

Programs that manipulate tree-shaped data structures often require complex, specialized proofs that are difficult to generalize and automate. This paper introduces a unified, foundational approach to verifying such programs. Central to our…

In this paper we show that checking satisfiability of a set of non-linear Horn clauses (also called a non-linear Horn clause program) can be achieved using a solver for linear Horn clauses. We achieve this by interleaving a program…

Verifying programs that manipulate tree data structures often requires complex, ad-hoc proofs that are hard to generalize and automate. This paper introduces an automatic technique for analyzing such programs. Our approach combines automata…

We address the problem of verifying the satisfiability of Constrained Horn Clauses (CHCs) based on theories of inductively defined data structures, such as lists and trees. We propose a transformation technique whose objective is the…

Catamorphisms are functions that are recursively defined on list and trees and, in general, on Algebraic Data Types (ADTs), and are often used to compute suitable abstractions of programs that manipulate ADTs. Examples of catamorphisms…

We address the problem of checking the satisfiability of a set of constrained Horn clauses (CHCs) possibly including more than one query. We propose a transformation technique that takes as input a set of CHCs, including a set of queries,…

We present Ultimate TreeAutomizer, a solver for satisfiability of sets of constrained Horn clauses. Constrained Horn clauses (CHC) are a fragment of first order logic with attractive properties in terms of expressiveness and accessibility…

A tree decomposition of the coordinates of a code is a mapping from the coordinate set to the set of vertices of a tree. A tree decomposition can be extended to a tree realization, i.e., a cycle-free realization of the code on the…

We address the problem of checking the satisfiability of Constrained Horn Clauses (CHCs) defined on Algebraic Data Types (ADTs), such as lists and trees. We propose a new technique for transforming CHCs defined on ADTs into CHCs where the…

The proof of a program property can be reduced to the proof of satisfiability of a set of constrained Horn clauses (CHCs) which can be automatically generated from the program and the property. In this paper we have conducted a case study…

Several techniques and tools have been developed for verification of properties expressed as Horn clauses with constraints over a background theory (CHC). Current CHC verification tools implement intricate algorithms and are often limited…

We present an approach to constrained Horn clause (CHC) verification combining three techniques: abstract interpretation over a domain of convex polyhedra, specialisation of the constraints in CHCs using abstract interpretation of…

This paper surveys recent work on applying analysis and transformation techniques that originate in the field of constraint logic programming (CLP) to the problem of verifying software systems. We present specialisation-based techniques for…

We introduce tree dimension and its leveled variant in order to measure the complexity of leaf sets in binary trees. We then provide a tight upper bound on the size of such sets using leveled tree dimension. This, in turn, implies both the…

Higher-order constrained Horn clauses (HoCHC) are a semantically-invariant system of higher-order logic modulo theories. With semi-decidable unsolvability over a semi-decidable background theory, HoCHC is suitable for safety verification.…

It is known that the verification of imperative, functional, and logic programs can be reduced to the satisfiability of constrained Horn clauses (CHCs), and this satisfiability check can be performed by using CHC solvers, such as Eldarica…

We formalize an existing computability-theoretic method of presenting first-order structures whose domains have the cardinality of the continuum. Work using these methods until now has emphasized their topological properties. We shift the…

Relational verification is a technique that aims at proving properties that relate two different program fragments, or two different program runs. It has been shown that constrained Horn clauses (CHCs) can effectively be used for relational…