Given a finite set of vectors over a finite totally ordered domain, we study the problem of computing a constraint in conjunctive normal form such that the set of solutions for the produced constraint is identical to the original set. We develop an efficient polynomial-time algorithm for the general case, followed by specific polynomial-time algorithms producing Horn, dual Horn, and bijunctive ...

In this paper, we study the problem of transient signal analysis. A signal-dependent algorithm is proposed which sequentially identifies the countable sets of decay rates and expansion coefficients present in a given signal. We qualitatively compare our method to existing techniques such as orthogonal exponential transforms generated from orthogonal polynomial classes. The presented algorithm h...

For many constraint satisfaction problems, there are well known, fast algorithms and functions that solve parts of the problem. Using these methods directly to solve the sub-problems signiicantly speeds up the solving process. Unfortunately, doing this has usually required the solver to be changed, or the correctness criteria to be reexamined. We describe a general mechanism to use procedures w...

We give a clear picture of the tractability/intractability frontier for quantified constraint satisfaction problems (QCSPs) under structural restrictions. On the negative side, we prove that checking QCSP satisfiability remains PSPACE-hard for all known structural properties more general than bounded treewidth and for the incomparable hypergraph acyclicity. Moreover, if the domain is not fixed,...

We systematically investigate the connections between constraint satisfaction problems, structures of bounded treewidth, and definability in logics with a finite number of variables. We first show that constraint satisfaction problems on inputs of treewidth less than k are definable using Datalog programs with at most k variables; this provides a new explanation for the tractability of these cl...

Establishing arc consistency on two relational structures is one of the most popular heuristics for the constraint satisfaction problem. We aim at determining the time complexity of arc consistency testing. The input structures G and H can be supposed to be connected colored graphs, as the general problem reduces to this particular case. We first observe the upper bound O(e(G)v(H) + v(G)e(H)), ...

Dechter et al. [5] proposed solving the Temporal Constraint Satisfaction Problem (TCSP) by modeling it as a metaCSP, which is a finite CSP with a unique global constraint. The size of this global constraint is exponential in the number of time points in the original TCSP, and generalized-arc consistency is equivalent to finding the minimal network of the TCSP, which is NP-hard. We introduce AC,...

This paper provides a technique for solving general constraint satisfaction problems (CSPs) with continuous variables. Constraints are represented by a hierarchical binary decomposition of the space of feasible values. We propose algorithms for pathand higher degrees of consistency based on logical operations defined on this representation and demonstrate that the algorithms terminate in polyno...

The performance of constraint based problem solving depends crucially on the problem representation. The same problem may be easy or diicult to solve depending on the way we formulate it. In this paper, we study reformu-lations of discrete constraint satisfaction problems (CSPs). We present a technique to transform a CSP P into its Boolean form, which allows us to nd diierent reformulations of ...

We determine the exact threshold of satisfiability for random instancesof a particular NP-complete constraint satisfaction problem (CSP). This isthe first random CSP model for which we have determined a precise linearsatisfiability threshold, and for which random instances with density nearthat threshold appear to be computationally difficult. More formally,it is the first r...