Recurrence with affine level mappings is P-time decidable for CLP(R)

In this paper we introduce a class of constraint logic programs such that their termination can be proved by using affine level mappings. We show that membership to this class is decidable in polynomial time.Comment: To appear in Theory and Practice of Logic Programming (TPLP

Restricted Space Algorithms for Isomorphism on Bounded Treewidth Graphs

The Graph Isomorphism problem restricted to graphs of bounded treewidth or bounded tree distance width are known to be solvable in polynomial time [Bod90],[YBFT99]. We give restricted space algorithms for these problems proving the following results: - Isomorphism for bounded tree distance width graphs is in L and thus complete for the class. We also show that for this kind of graphs a canon can be computed within logspace. - For bounded treewidth graphs, when both input graphs are given together with a tree decomposition, the problem of whether there is an isomorphism which respects the decompositions (i.e. considering only isomorphisms mapping bags in one decomposition blockwise onto bags in the other decomposition) is in L. - For bounded treewidth graphs, when one of the input graphs is given with a tree decomposition the isomorphism problem is in LogCFL. - As a corollary the isomorphism problem for bounded treewidth graphs is in LogCFL. This improves the known TC1 upper bound for the problem given by Grohe and Verbitsky [GroVer06].Comment: STACS conference 2010, 12 page

Quantum algorithms for classical lattice models

We give efficient quantum algorithms to estimate the partition function of (i) the six vertex model on a two-dimensional (2D) square lattice, (ii) the Ising model with magnetic fields on a planar graph, (iii) the Potts model on a quasi 2D square lattice, and (iv) the Z_2 lattice gauge theory on a three-dimensional square lattice. Moreover, we prove that these problems are BQP-complete, that is, that estimating these partition functions is as hard as simulating arbitrary quantum computation. The results are proven for a complex parameter regime of the models. The proofs are based on a mapping relating partition functions to quantum circuits introduced in [Van den Nest et al., Phys. Rev. A 80, 052334 (2009)] and extended here.Comment: 21 pages, 12 figure

Optimal Embedding of Functions for In-Network Computation: Complexity Analysis and Algorithms

We consider optimal distributed computation of a given function of distributed data. The input (data) nodes and the sink node that receives the function form a connected network that is described by an undirected weighted network graph. The algorithm to compute the given function is described by a weighted directed acyclic graph and is called the computation graph. An embedding defines the computation communication sequence that obtains the function at the sink. Two kinds of optimal embeddings are sought, the embedding that---(1)~minimizes delay in obtaining function at sink, and (2)~minimizes cost of one instance of computation of function. This abstraction is motivated by three applications---in-network computation over sensor networks, operator placement in distributed databases, and module placement in distributed computing. We first show that obtaining minimum-delay and minimum-cost embeddings are both NP-complete problems and that cost minimization is actually MAX SNP-hard. Next, we consider specific forms of the computation graph for which polynomial time solutions are possible. When the computation graph is a tree, a polynomial time algorithm to obtain the minimum delay embedding is described. Next, for the case when the function is described by a layered graph we describe an algorithm that obtains the minimum cost embedding in polynomial time. This algorithm can also be used to obtain an approximation for delay minimization. We then consider bounded treewidth computation graphs and give an algorithm to obtain the minimum cost embedding in polynomial time

A Trichotomy in the Complexity of Counting Answers to Conjunctive Queries

Conjunctive queries are basic and heavily studied database queries; in relational algebra, they are the select-project-join queries. In this article, we study the fundamental problem of counting, given a conjunctive query and a relational database, the number of answers to the query on the database. In particular, we study the complexity of this problem relative to sets of conjunctive queries. We present a trichotomy theorem, which shows essentially that this problem on a set of conjunctive queries is either tractable, equivalent to the parameterized CLIQUE problem, or as hard as the parameterized counting CLIQUE problem; the criteria describing which of these situations occurs is simply stated, in terms of graph-theoretic conditions

Cryptography from tensor problems

We describe a new proposal for a trap-door one-way function. The new proposal belongs to the "multivariate quadratic" family but the trap-door is different from existing methods, and is simpler