Related papers: Defunctionalization of Higher-Order Constrained Ho…

Constrained Horn Clauses (CHCs) have conventionally been used as a low-level representation in formal verification. Most existing solvers use a diverse set of specialized techniques, including direct state space traversal or…

We present a recursive formulation of the Horn algorithm for deciding the satisfiability of propositional clauses. The usual presentations in imperative pseudo-code are informal and not suitable for simple proofs of its main properties. By…

In deduction modulo, a theory is not represented by a set of axioms but by a congruence on propositions modulo which the inference rules of standard deductive systems---such as for instance natural deduction---are applied. Therefore, the…

One of the main challenges in software verification is efficient and precise compositional analysis of programs with procedures and loops. Interpolation methods remain one of the most promising techniques for such verification, and are…

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 propose a novel method for inferring refinement types of higher-order functional programs. The main advantage of the proposed method is that it can infer maximally preferred (i.e., Pareto optimal) refinement types with respect to a…

Recent years have witness remarkable performance improvements in maximum satisfiability (MaxSAT) solvers. In practice, MaxSAT algorithms often target the most generic MaxSAT formulation, whereas dedicated solvers, which address specific…

We show how automatic tools for the verification of linear and branching time properties of procedural, multi-threaded, and functional programs as well as program synthesis can be naturally and uniformly seen as solvers of constraints in…

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…

Many transformation techniques developed for constraint logic programs, also known as constrained Horn clauses (CHCs), have found new useful applications in the field of program verification. In this paper, we work out a nontrivial case…

We define a new class of set functions that in addition to being monotone and subadditive, also admit a very limited form of submodularity defined over a permutation of the ground set. We refer to this permutation as a submodular order.…

The monadic shallow linear Horn fragment is well-known to be decidable and has many application, e.g., in security protocol analysis, tree automata, or abstraction refinement. It was a long standing open problem how to extend the fragment…

Many Program Verification and Synthesis problems of interest can be modeled directly using Horn clauses and many recent advances in the CLP and CAV communities have centered around efficiently solving problems presented as Horn clauses. The…

We study abduction in First Order Horn logic theories where all atoms can be abduced and we are looking for preferred solutions with respect to three objective functions: cardinality minimality, coherence, and weighted abduction. We…

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…

Horn-satisfiability or Horn-SAT is the problem of deciding whether a satisfying assignment exists for a Horn formula, a conjunction of clauses each with at most one positive literal (also known as Horn clauses). It is a well-known…

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…

Higher-order tensor methods were recently proposed for minimizing smooth convex and nonconvex functions. Higher-order algorithms accelerate the convergence of the classical first-order methods thanks to the higher-order derivatives used in…

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…

This paper presents a verification framework based on a new class of predicate Constraint Satisfaction Problems called pCSP where constraints are represented as clauses modulo first-order theories over function variables and predicate…