This thesis designs a theoretical and general framework where proof-search can modularly interact with domain-specific procedure(s). This framework is a focussed sequent calculus for polarised classical logic, with quantifiers, and it is designed in the view of capturing various computer-aided reasoning techniques that exist in logic programing, goal-directed systems, proof-assistants, and auto...

Recent experimental results have shown that the strength of resolution, the propositional DPLL procedure, the KSAT procedure for description logics, or related tableau-like implementations such as DLP, is due to reduction rules which propagate constraints and prune the search space. Yet, for first order logic such reduction rules are only known for resolution. The lack of reduction rules for fi...

In this paper we relate different formulations of the DPLL(T ) procedure. The first formulation is that of [NOT06] based on a system of rewrite rules, which we denote DPLL(T ). The second formulation is an inference system of [Tin02], which we denote LKDPLL(T ). The third formulation is the application of a standard proof-search mechanism in a sequent calculus LK(T ) introduced here. We formali...

This paper reports our work on application of concurrent/distributed techniques to SAT. These were investigated using each of the following methods: the DPLL [5] algorithm, the dilemma rule of the Stålmarck’s algorithm [12] and a concurrent/distributed hybrid SAT solver: DPLL-Stålmarck, using a combination of the DPLL and the dilemma rule based algorithm. The prototypes have been implemented us...

Many problems can be specified by patterns of propositional formulae depending on a parameter, e.g. the specification of a circuit usually depends on the number of bits of its input. We define a logic whose formulae, called iterated schemata, allow to express such patterns. i=1 or n i=1 (called iterations) where n is an (unbound) integer variable called a parameter. The expressive power of iter...

This paper discusses a model of constraint satisfaction problems known as uniquely extendible constraint satisfaction problems. This model includes and generalizes XOR-SAT, and the model includes an NP-complete problem that appears to share many of the threshold characteristics of random SAT. In this paper we find an exact threshold in the behavior of two versions of DPLL on random instances of...

A versatile, low-cost, digital signal processor (DSP) based lock-in module with external reference is described. This module is used to implement an industrial spectrophotometer for measuring spectral transmission and reflection of automotive and architectonic coating glasses over the ultraviolet, visible and near-infrared wavelength range. The light beams are modulated with an optical chopper....

In this paper we relate different formulations of the DPLL(T ) procedure. The first formulation is that of [NOT06] based on a system of rewrite rules, which we denote DPLL(T ). The second formulation is an inference system of [Tin02], which we denote LKDPLL(T ). The third formulation is the application of a standard proof-search mechanism in a sequent calculus LK(T ) introduced here. We formali...