A negative database is a representation of all elements not contained in a given database. A negative database can enhance the privacy of sensitive information without resorting to encryption. This can be useful in settings where encryption is too expensive, e.g., some sensor networks, or for applications where searches or other operations on stored data are desired. The original negative database framework supported only authentication queries and operations for modifying data, such as insert and delete. This paper extends that work by defining a set of relational operators for negative representations. For each relational operator, the corresponding negative operator is defined such that the result of the negative operator applied to a negative representation is equivalent to the positive version applied to the positive representation. Algorithms for each relational operator are described and compared to its positive counterpart. This work enhances the practicality of negative databases and expands their range of application. 1.

Abstract. Nogood recording is a well known technique for reducing the thrashing encountered by tree search algorithms. One of the most significant disadvantages of nogood recording has been its prohibitive space complexity. In this paper we attempt to mitigate this by using an automaton to compactly represent a set of nogoods. We demonstrate how nogoods can be propagated using a known algorithm for achieving generalised arc consistency. Our experimental results on a number of benchmark problems demonstrate the utility of our approach. 1

Abstract. Often when modelling systems, physical constraints on the resources available are needed. For example, we might say that at most N processes can access a particular resource at any moment or exactly M participants are needed for an agreement. Such situations are concisely modelled where propositions are constrained such that at most N, or exactly M, can hold at any moment in time. This paper describes both the logical basis and a verification method for propositional linear time temporal logics which allow such constraints as input. The method incorporates ideas developed earlier for a resolution method for the temporal logic TLX and a tableaux-like procedure for PTL. The complexity of this procedure is discussed and case studies are examined. The logic itself represents a combination of standard temporal logic with classical constraints restricting the numbers of propositions that can be satisfied at any moment in time. 1

Abstract. In this paper we show that the power of using k-consistency techniques in a constraint problem is precisely captured by using a particular inference rule, which we call positive-hyper-resolution, on the direct Boolean encoding of the CSP instance. We also show that current clauselearning SAT-solvers will deduce any positive-hyper-resolvent of a fixed size from a given set of clauses in polynomial expected time. We combine these two results to show that, without being explicitly designed to do so, current clause-learning SAT-solvers efficiently simulate k-consistency techniques, for all values of k. We then give some experimental results to show that this feature allows clause-learning SAT-solvers to efficiently solve certain families of CSP instances which are challenging for conventional CP solvers. 1

Computer tools are needed in systems biology to analyse qualitatively the dynamics of Gene Regulatory Networks (GRNs). Particularly, biologists are interested in infering these networks from observed behaviours. In this paper we present a Boolean satisfiability (SAT) approach applied on a widely used asynchronous logical description of such networks. After a brief presentation of the asynchronous logical formalism, we explain how we express into constraints the evolution rule of GRNs. Then, we show how to translate efficiently these constraints into Boolean formulae. We finally report results about infering parameters of a biological model of the λ-phage immunity control. Our study shows that SAT solving is a powerful tool for analysing GRNs and related transition systems found in biological applications. 1

Most, if not all, state-of-the-art complete SAT solvers are complex variations of the DPLL procedure described in the early 1960’s. Published descriptions of these modern algorithms and related data structures are given either as high-level (rule-based) transition systems or, informally, as (pseudo) programming language code. The former, although often accompanied with (informal) correctness proofs, are usually very abstract and do not specify many details crucial for efficient implementation. The latter usually do not involve any correctness argument and the given code is often hard to understand and modify. This paper aims at bridging this gap: we present SAT solving algorithms that are formally proved correct, but at the same time they contain information required for efficient implementation. We use a tutorial, top-down, approach and develop a SAT solver, starting from a simple design that is subsequently extended, step-by-step, with the requisite series of features. Heuristic parts of the solver are abstracted away, since they usually do not affect solver correctness (although they are very important for efficiency). All algorithms are given in pseudo-code. The code is accompanied with correctness conditions, given in Hoare logic style. Correctness proofs are formalized within the Isabelle theorem proving system and are available in the extended version of this paper. The given pseudo-code served as a basis for our SAT solver argo-sat.

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Abstract. In this paper, we want to handle multiple interleaved Alldiff constraints from two points of view: a uniform propagation framework with some CSP reduction rules and a SAT encoding of these rules that preserves the reduction properties of CSP. 1

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Reactive search for MAX-SAT: diversification-bias properties with prohibitions and penalties