Constraint Propagation in Presence of Arrays

We describe the use of array expressions as constraints, which represents a consequent generalisation of the "element" constraint. Constraint propagation for array constraints is studied theoretically, and for a set of domain reduction rules the local consistency they enforce, arc-consistency, is proved. An efficient algorithm is described that encapsulates the rule set and so inherits the capability to enforce arc-consistency from the rules.Comment: 10 pages. Accepted at the 6th Annual Workshop of the ERCIM Working Group on Constraints, 200

On the Implementation of GNU Prolog

GNU Prolog is a general-purpose implementation of the Prolog language, which distinguishes itself from most other systems by being, above all else, a native-code compiler which produces standalone executables which don't rely on any byte-code emulator or meta-interpreter. Other aspects which stand out include the explicit organization of the Prolog system as a multipass compiler, where intermediate representations are materialized, in Unix compiler tradition. GNU Prolog also includes an extensible and high-performance finite domain constraint solver, integrated with the Prolog language but implemented using independent lower-level mechanisms. This article discusses the main issues involved in designing and implementing GNU Prolog: requirements, system organization, performance and portability issues as well as its position with respect to other Prolog system implementations and the ISO standardization initiative.Comment: 30 pages, 3 figures, To appear in Theory and Practice of Logic Programming (TPLP); Keywords: Prolog, logic programming system, GNU, ISO, WAM, native code compilation, Finite Domain constraint

Branch-and-Prune Search Strategies for Numerical Constraint Solving

When solving numerical constraints such as nonlinear equations and inequalities, solvers often exploit pruning techniques, which remove redundant value combinations from the domains of variables, at pruning steps. To find the complete solution set, most of these solvers alternate the pruning steps with branching steps, which split each problem into subproblems. This forms the so-called branch-and-prune framework, well known among the approaches for solving numerical constraints. The basic branch-and-prune search strategy that uses domain bisections in place of the branching steps is called the bisection search. In general, the bisection search works well in case (i) the solutions are isolated, but it can be improved further in case (ii) there are continuums of solutions (this often occurs when inequalities are involved). In this paper, we propose a new branch-and-prune search strategy along with several variants, which not only allow yielding better branching decisions in the latter case, but also work as well as the bisection search does in the former case. These new search algorithms enable us to employ various pruning techniques in the construction of inner and outer approximations of the solution set. Our experiments show that these algorithms speed up the solving process often by one order of magnitude or more when solving problems with continuums of solutions, while keeping the same performance as the bisection search when the solutions are isolated.Comment: 43 pages, 11 figure

On the Sample Complexity of Multichannel Frequency Estimation via Convex Optimization

The use of multichannel data in line spectral estimation (or frequency estimation) is common for improving the estimation accuracy in array processing, structural health monitoring, wireless communications, and more. Recently proposed atomic norm methods have attracted considerable attention due to their provable superiority in accuracy, flexibility and robustness compared with conventional approaches. In this paper, we analyze atomic norm minimization for multichannel frequency estimation from noiseless compressive data, showing that the sample size per channel that ensures exact estimation decreases with the increase of the number of channels under mild conditions. In particular, given $L$ channels, order $K\left(\log K\right) \left(1+\frac{1}{L}\log N\right)$ samples per channel, selected randomly from $N$ equispaced samples, suffice to ensure with high probability exact estimation of $K$ frequencies that are normalized and mutually separated by at least $\frac{4}{N}$. Numerical results are provided corroborating our analysis.Comment: 14 pages, double column, to appear in IEEE Trans. Information Theor

Specialising finite domain programs with polyhedra

A procedure is described for tightening domain constraints of finite domain logic programs by applying a static analysis based on convex polyhedra. Individual finite domain constraints are over-approximated by polyhedra to describe the solution space over ninteger variables as an n dimensional polyhedron. This polyhedron is then approximated, using projection, as an n dimensional bounding box that can be used to specialise and improve the domain constraints. The analysis can be implemented straightforwardly and an empirical evaluation of the specialisation technique is given

Counting, generating and sampling tree alignments

Pairwise ordered tree alignment are combinatorial objects that appear in RNA secondary structure comparison. However, the usual representation of tree alignments as supertrees is ambiguous, i.e. two distinct supertrees may induce identical sets of matches between identical pairs of trees. This ambiguity is uninformative, and detrimental to any probabilistic analysis.In this work, we consider tree alignments up to equivalence. Our first result is a precise asymptotic enumeration of tree alignments, obtained from a context-free grammar by mean of basic analytic combinatorics. Our second result focuses on alignments between two given ordered trees $S$ and $T$. By refining our grammar to align specific trees, we obtain a decomposition scheme for the space of alignments, and use it to design an efficient dynamic programming algorithm for sampling alignments under the Gibbs-Boltzmann probability distribution. This generalizes existing tree alignment algorithms, and opens the door for a probabilistic analysis of the space of suboptimal RNA secondary structures alignments.Comment: ALCOB - 3rd International Conference on Algorithms for Computational Biology - 2016, Jun 2016, Trujillo, Spain. 201