Related papers: Multiple Query Satisfiability of Constrained Horn …
Alternation of forward and backward analyses is a standard technique in abstract interpretation of programs, which is in particular useful when we wish to prove unreachability of some undesired program states. The current state-of-the-art…
We present a simple resolution proof system for higher-order constrained Horn clauses (HoCHC) - a system of higher-order logic modulo theories - and prove its soundness and refutational completeness w.r.t. the standard semantics. As…
Verification conditions (VCs) are logical formulas whose satisfiability guarantees program correctness. We consider VCs in the form of constrained Horn clauses (CHC) which are automatically generated from the encoding of (an interpreter of)…
The use of temporal logics has long been recognised as a fundamental approach to the formal specification and verification of reactive systems. In this paper, we take on the problem of automatically verifying a temporal property, given by a…
This paper tackles the problem of the existence of solutions for recursive systems of Horn clauses with second-order variables interpreted as integer relations, and harnessed by quantifier-free difference bounds arithmetic. We start by…
We present a compositional SMT-based algorithm for safety of procedural C programs that takes the heap into consideration as well. Existing SMT-based approaches are either largely restricted to handling linear arithmetic operations and…
The quantified constraint satisfaction problem $\mathrm{QCSP}(\mathcal{A})$ is the problem to decide whether a positive Horn sentence, involving nothing more than the two quantifiers and conjunction, is true on some fixed structure…
We present a method for verifying properties of time-aware business processes, that is, business process where time constraints on the activities are explicitly taken into account. Business processes are specified using an extension of the…
A definite Horn theory is a set of n-dimensional Boolean vectors whose characteristic function is expressible as a definite Horn formula, that is, as conjunction of definite Horn clauses. The class of definite Horn theories is known to be…
The monadic shallow linear (MSL) class is a decidable fragment of first-order Horn clauses that was discovered and rediscovered around the turn of the century, with applications in static analysis and verification. We propose a new class of…
The constraint satisfaction problem (CSP) involves deciding, given a set of variables and a set of constraints on the variables, whether or not there is an assignment to the variables satisfying all of the constraints. One formulation of…
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…
We design learning algorithms for synthesizing invariants using Horn implication counterexamples (Horn-ICE), extending the ICE-learning model. In particular, we describe a decision-tree learning algorithm that learns from Horn-ICE samples,…
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…
To help a user specify and verify quantified queries --- a class of database queries known to be very challenging for all but the most expert users --- one can question the user on whether certain data objects are answers or non-answers to…
We describe simple algebraic and combinatorial characterisations of finite relational core structures admitting finitely many obstructions. As a consequence, we show that it is decidable to determine whether a constraint satisfaction…
We investigate the enumeration of varieties of boolean theories related to Horn clauses. We describe a number of combinatorial equivalences among different characterizations and calculate the number of different theories in $n$ variables…
Despite decades of research, there are still a number of concepts commonly found in software programs that are considered challenging for verification: among others, such concepts include concurrency, and the compositional analysis of…
In this paper we discuss the optimizing compilation of Constraint Handling Rules (CHRs). CHRs are a multi-headed committed choice constraint language, commonly applied for writing incremental constraint solvers. CHRs are usually implemented…
We present initial limit Datalog, a new extensible class of constrained Horn clauses for which the satisfiability problem is decidable. The class may be viewed as a generalisation to higher-order logic (with a simple restriction on types)…