ILP Modulo Data

The vast quantity of data generated and captured every day has led to a pressing need for tools and processes to organize, analyze and interrelate this data. Automated reasoning and optimization tools with inherent support for data could enable advancements in a variety of contexts, from data-backed decision making to data-intensive scientific research. To this end, we introduce a decidable logic aimed at database analysis. Our logic extends quantifier-free Linear Integer Arithmetic with operators from Relational Algebra, like selection and cross product. We provide a scalable decision procedure that is based on the BC(T) architecture for ILP Modulo Theories. Our decision procedure makes use of database techniques. We also experimentally evaluate our approach, and discuss potential applications.Comment: FMCAD 2014 final version plus proof

In silico estimation of annealing specificity of query searches in DNA databases

We consider DNA implementations of databases for digital signals with retrieval and mining capabilities. Digital signals are encoded in DNA sequences and retrieved through annealing between query DNA primers and data carrying DNA target sequences. The hybridization between query and target can be non-specific containing multiple mismatches thus implementing similarity-based searches. In this paper we examine theoretically and by simulation the efficiency of such a system by estimating the concentrations of query-target duplex formations at equilibrium. A coupled kinetic model is used to estimate the concentrations. We offer a derivation that results in an equation that is guaranteed to have a solution and can be easily and accurately solved computationally with bi-section root-finding methods. Finally, we also provide an approximate solution at dilute query concentrations that results in a closed form expression. This expression is used to improve the speed of the bi-section algorithm and also to find a closed form expression for the specificity ratios

On Incomplete XML Documents with Integrity Constraints

Abstract. We consider incomplete specifications of XML documents in the presence of schema information and integrity constraints. We show that integrity constraints such as keys and foreign keys affect consistency of such specifications. We prove that the consistency problem for incomplete specifications with keys and foreign keys can always be solved in NP. We then show a dichotomy result, classifying the complexity of the problem as NP-complete or PTIME, depending on the precise set of features used in incomplete descriptions.

The DLV System for Knowledge Representation and Reasoning

This paper presents the DLV system, which is widely considered the state-of-the-art implementation of disjunctive logic programming, and addresses several aspects. As for problem solving, we provide a formal definition of its kernel language, function-free disjunctive logic programs (also known as disjunctive datalog), extended by weak constraints, which are a powerful tool to express optimization problems. We then illustrate the usage of DLV as a tool for knowledge representation and reasoning, describing a new declarative programming methodology which allows one to encode complex problems (up to $\Delta^P_3$-complete problems) in a declarative fashion. On the foundational side, we provide a detailed analysis of the computational complexity of the language of DLV, and by deriving new complexity results we chart a complete picture of the complexity of this language and important fragments thereof. Furthermore, we illustrate the general architecture of the DLV system which has been influenced by these results. As for applications, we overview application front-ends which have been developed on top of DLV to solve specific knowledge representation tasks, and we briefly describe the main international projects investigating the potential of the system for industrial exploitation. Finally, we report about thorough experimentation and benchmarking, which has been carried out to assess the efficiency of the system. The experimental results confirm the solidity of DLV and highlight its potential for emerging application areas like knowledge management and information integration.Comment: 56 pages, 9 figures, 6 table

Constraint Satisfaction and Semilinear Expansions of Addition over the Rationals and the Reals

A semilinear relation is a finite union of finite intersections of open and closed half-spaces over, for instance, the reals, the rationals, or the integers. Semilinear relations have been studied in connection with algebraic geometry, automata theory, and spatiotemporal reasoning. We consider semilinear relations over the rationals and the reals. Under this assumption, the computational complexity of the constraint satisfaction problem (CSP) is known for all finite sets containing R+={(x,y,z) | x+y=z}, <=, and {1}. These problems correspond to expansions of the linear programming feasibility problem. We generalise this result and fully determine the complexity for all finite sets of semilinear relations containing R+. This is accomplished in part by introducing an algorithm, based on computing affine hulls, which solves a new class of semilinear CSPs in polynomial time. We further analyse the complexity of linear optimisation over the solution set and the existence of integer solutions.Comment: 22 pages, 1 figur

Compressed Representations of Conjunctive Query Results

Relational queries, and in particular join queries, often generate large output results when executed over a huge dataset. In such cases, it is often infeasible to store the whole materialized output if we plan to reuse it further down a data processing pipeline. Motivated by this problem, we study the construction of space-efficient compressed representations of the output of conjunctive queries, with the goal of supporting the efficient access of the intermediate compressed result for a given access pattern. In particular, we initiate the study of an important tradeoff: minimizing the space necessary to store the compressed result, versus minimizing the answer time and delay for an access request over the result. Our main contribution is a novel parameterized data structure, which can be tuned to trade off space for answer time. The tradeoff allows us to control the space requirement of the data structure precisely, and depends both on the structure of the query and the access pattern. We show how we can use the data structure in conjunction with query decomposition techniques, in order to efficiently represent the outputs for several classes of conjunctive queries.Comment: To appear in PODS'18; 35 pages; comments welcom