Linear Datalog Program Research Articles

A linear algebraic approach to datalog evaluation

AbstractWe propose a fundamentally new approach to Datalog evaluation. Given a linear Datalog program DB written usingNconstants and binary predicates, we first translate if-and-only-if completions of clauses in DB into a setEq(DB) of matrix equations with a non-linear operation, where relations inMDB, the least Herbrand model of DB, are encoded as adjacency matrices. We then translateEq(DB) into another, but purely linear matrix equationsẼq(DB). It is proved that the least solution ofẼq(DB) in the sense of matrix ordering is converted to the least solution ofEq(DB) and the latter givesMDBas a set of adjacency matrices. Hence, computing the least solution ofẼq(DB) is equivalent to computingMDBspecified by DB. For a class of tail recursive programs and for some other types of programs, our approach achievesO(N3) time complexity irrespective of the number of variables in a clause since only matrix operations costingO(N3) or less are used. We conducted two experiments that compute the least Herbrand models of linear Datalog programs. The first experiment computes transitive closure of artificial data and real network data taken from the Koblenz Network Collection. The second one compared the proposed approach with the state-of-the-art symbolic systems including two Prolog systems and two ASP systems, in terms of computation time for a transitive closure program and the same generation program. In the experiment, it is observed that our linear algebraic approach runs 101~ 104times faster than the symbolic systems when data is not sparse. Our approach is inspired by the emergence of big knowledge graphs and expected to contribute to the realization of rich and scalable logical inference for knowledge graphs.

Caterpillar Dualities and Regular Languages

We characterize obstruction sets in caterpillar dualities in terms of regular languages and give a construction of the dual of a regular family of caterpillars. In particular, we prove that every monadic linear Datalog program with at most one extensional database per rule defines the complement of a contraint satisfaction problem.

Linear Datalog and Bounded Path Duality of Relational Structures

In this paper we systematically investigate the connections between logics with a finite number of variables, structures of bounded pathwidth, and linear Datalog Programs. We prove that, in the context of Constraint Satisfaction Problems, all these concepts correspond to different mathematical embodiments of a unique robust notion that we call bounded path duality. We also study the computational complexity implications of the notion of bounded path duality. We show that every constraint satisfaction problem $\csp(\best)$ with bounded path duality is solvable in NL and that this notion explains in a uniform way all families of CSPs known to be in NL. Finally, we use the results developed in the paper to identify new problems in NL.

Linearisability on datalog programs

Linear Datalog programs are programs whose clauses have at most one intensional atom in their bodies. We explore syntactic classes of Datalog programs (syntactically non-linear) which turn out to express no more than the queries expressed by linear Datalog programs. In particular, we investigate linearisability of (database queries corresponding to) piecewise linear Datalog programs and chain queries: (a) We prove that piecewise linear Datalog programs can always be transformed into linear Datalog programs, by virtue of a procedure which performs the transformation automatically. The procedure relies upon conventional logic program transformation techniques. (b) We identify a new class of linearisable chain queries, referred to as pseudo-regular, and prove their linearisability constructively, by generating, for any given pseudo-regular chain query, the Datalog program corresponding to it.