Related papers: The Relationship between Craig Interpolation and R…
We present HornStr, the first solver for invariant synthesis for Regular Model Checking (RMC) with the specification provided in the SMT-LIB 2.6 theory of strings. It is well-known that invariant synthesis for RMC subsumes various important…
We consider approximating data structures with collections of the items that they contain. For examples, lists, binary trees, tuples, etc, can be approximated by sets or multisets of the items within them. Such approximations can be used to…
In this paper we develop cyclic proof systems for the problem of inclusion between the least sets of models of mutually recursive predicates, when the ground constraints in the inductive definitions belong to the quantifier-free fragments…
This is a survey on propositional proof complexity aimed at introducing the basics of the field with a particular focus on a method known as feasible interpolation. This method is used to construct "hard theorems" for several proof systems…
We introduce new methods of equivalence checking and simulation based on Computing Range Reduction (CRR). Given a combinational circuit $N$, the CRR problem is to compute the set of outputs that disappear from the range of $N$ if a set of…
We formalise and mechanise a construtive, proof theoretic proof of Craig's Interpolation Theorem in Isabelle/HOL. We give all the definitions and lemma statements both formally and informally. We also transcribe informally the formal…
Tabled Constraint Logic Programming is a powerful execution mechanism for dealing with Constraint Logic Programming without worrying about fixpoint computation. Various applications, e.g in the fields of program analysis and model checking,…
Graph transformation systems (GTS) and constraint handling rules (CHR) are non-deterministic rule-based state transition systems. CHR is well-known for its powerful confluence and program equivalence analyses, for which we provide the basis…
Software development depends on the use of libraries whose public specifications inform client code and impose obligations on private implementations; it follows that verification at scale must also be modular, preserving such abstraction.…
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…
Recovering concurrency structure directly from source code is difficult because shared-resource identity and protection relations are often obscured by aliasing, ownership, and API-specific idioms. We therefore study a specification-driven,…
As a generalization of Hermite interpolation problem, Birkhoff interpolation is an important subject in numerical approximation. This paper generalizes the existing Generalized Recursive Polynomial Interpolation Algorithm (GRPIA) that is…
We consider constrained Horn clause solving from the more general point of view of solving formula equations. Constrained Horn clauses correspond to the subclass of Horn formula equations. We state and prove a fixed-point theorem for Horn…
We introduce the framework FreeCHR which formalizes the embedding of Constraint Handling Rules (CHR) into a host language, using the concept of initial algebra semantics from category theory. We hereby establish a high-level implementation…
Nonlinear interpolants have been shown useful for the verification of programs and hybrid systems in contexts of theorem proving, model checking, abstract interpretation, etc. The underlying synthesis problem, however, is challenging and…
Program transformation is an appealing technique which allows to improve run-time efficiency, space-consumption, and more generally to optimize a given program. Essentially, it consists of a sequence of syntactic program manipulations which…
The article "Interpolation and SAT-Based Model Checking" (McMillan, 2003) describes a formal-verification algorithm, which was originally devised to verify safety properties of finite-state transition systems. It derives interpolants from…
We describe and explore so-called linear hash functions and show how they can be used to build error detection and correction codes. The method can be applied for different types of errors (for example, burst errors). When the method is…
Effective verification and validation techniques for modern scientific machine learning workflows are challenging to devise. Statistical methods are abundant and easily deployed, but often rely on speculative assumptions about the data and…
Hoare-style inference rules for program constructs permit the copying of expressions and tests from program text into logical contexts. It is known that this requires care even for sequential programs but much more serious issues arise with…