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The use of interpolants in model checking is becoming an enabling technology to allow fast and robust verification of hardware and software. The application of encodings based on the theory of arrays, however, is limited by the…
Interpolation is an essential tool in software verification, where first-order theories are used to constrain datatypes manipulated by programs. In this paper, we introduce the datatype theory of contiguous arrays with maxdiff, where arrays…
An algorithm for generating interpolants for formulas which are conjunctions of quadratic polynomial inequalities (both strict and nonstrict) is proposed. The algorithm is based on a key observation that quadratic polynomial inequalities…
Multilinear interpolation is a powerful tool used in obtaining strong type boundedness for a variety of operators assuming only a finite set of restricted weak-type estimates. A typical situation occurs when one knows that a multilinear…
In this paper we study possibilities of interpolation and symbol elimination in extensions of a theory $\mathcal{T}_0$ with additional function symbols whose properties are axiomatised using a set of clauses. We analyze situations in which…
Interpolation of jointly infeasible predicates plays important roles in various program verification techniques such as invariant synthesis and CEGAR. Intrigued by the recent result by Dai et al.\ that combines real algebraic geometry and…
Craig interpolation is a fundamental property of classical and non-classic logics with a plethora of applications from philosophical logic to computer-aided verification. The question of which interpolants can be obtained from an…
In ESOP 2008, Gulwani and Musuvathi introduced a notion of cover and exploited it to handle infinite-state model checking problems. Motivated by applications to the verification of data-aware processes, we proved in a previous paper that…
Software model checking is a challenging problem, and generating relevant invariants is a key factor in proving the safety properties of a program. Program invariants can be obtained by various approaches, including lightweight procedures…
A logic has uniform interpolation if its formulas can be projected down to given subsignatures, preserving all logical consequences that do not mention the removed symbols; the weaker property of (Craig) interpolation allows the projected…
We study quantifiers and interpolation properties in \emph{orthologic}, a non-distributive weakening of classical logic that is sound for formula validity with respect to classical logic, yet has a quadratic-time decision procedure. We…
Interpolation-based techniques have been widely and successfully applied in the verification of hardware and software, e.g., in bounded-model check- ing, CEGAR, SMT, etc., whose hardest part is how to synthesize interpolants. Various work…
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…
Craig interpolation has emerged as an effective means of generating candidate program invariants. We present interpolation procedures for the theories of Presburger arithmetic combined with (i) uninterpreted predicates (QPA+UP), (ii)…
Craig interpolation has become a versatile algorithmic tool for improving software verification. Interpolants can, for instance, accelerate the convergence of fixpoint computations for infinite-state systems. They also help improve the…
This chapter provides a comprehensive overview of proof-theoretic methods for establishing interpolation properties across a range of logics, including classical, intuitionistic, modal, and substructural logics. Central to the discussion…
In this paper, we develop the theory of bi-freeness in an amalgamated setting. We construct the operator-valued bi-free cumulant functions, and show that the vanishing of mixed cumulants is necessary and sufficient for bi-free independence.…
We define a notion of general uniform interpolant, generalizing the notions of cover and of uniform interpolant and identify situations in which symbol elimination can be used for computing general uniform interpolants. We investigate the…
The concept of uniform interpolant for a quantifier-free formula from a given formula with a list of symbols, while well-known in the logic literature, has been unknown to the formal methods and automated reasoning community for a long…
Information-theoretic quantities like entropy and mutual information have found numerous uses in machine learning. It is well known that there is a strong connection between these entropic quantities and submodularity since entropy over a…