An interpolating family of means

An Interpolating Family of Means

This paper is concerned with a new family of binary symmetric means mp of two positive numbers a and b: 1 mp(a, b) = cp ∫ ∞ 0 dx [(xp + ap)(xp + bp)]1/p , 0 < p < ∞, where the constant cp, depending on p, is chosen to have mp(a, a) = a. Two distinctive members in the family are the well-known logarithmic mean (p = 1) and arithmeticgeometric mean (p = 2). Different expressions for mp are obtaine...

An Interpolating Theorem Prover

We present a method of deriving Craig interpolants from proofs in the quantifier-free theory of linear inequality and uninterpreted function symbols, and an interpolating theorem prover based on this method. The prover has been used for predicate refinement in the Blast software model checker, and can also be used directly for model checking infinite-state systems, using interpolation-based ima...

Merit: An Interpolating Model-Checker

We present the tool MERIT, a CEGAR model-checker for safety properties of counter-systems, which sits in the Lazy Abstraction with Interpolants (LAWI) framework. LAWI is parametric with respect to the interpolation technique and so is MERIT. Thanks to its open architecture, MERIT makes it possible to experiment new refinement techniques without having to re-implement the generic, technical part...

SMTInterpol: An Interpolating SMT Solver

Craig interpolation is an active research topic and has become a powerful technique in verification. We present SMTInterpol, an interpolating SMT solver for the quantifier-free fragment of the combination of the theory of uninterpreted functions and the theory of linear arithmetic over integers and reals. SMTInterpol is SMTLIB 2 compliant and available under an open source software license (LGP...

AN Lp DEFINITION OF INTERPOLATING BLASCHKE PRODUCTS