22,787 research outputs found
Learning definite Horn formulas from closure queries
A definite Horn theory is a set of n-dimensional Boolean vectors whose characteristic function is expressible as a definite Horn formula, that is, as conjunction of definite Horn clauses. The class of definite Horn theories is known to be learnable under different query learning settings, such as learning from membership and equivalence queries or learning from entailment. We propose yet a different type of query: the closure query. Closure queries are a natural extension of membership queries and also a variant, appropriate in the context of definite Horn formulas, of the so-called correction queries. We present an algorithm that learns conjunctions of definite Horn clauses in polynomial time, using closure and equivalence queries, and show how it relates to the canonical Guigues–Duquenne basis for implicational systems. We also show how the different query models mentioned relate to each other by either showing full-fledged reductions by means of query simulation (where possible), or by showing their connections in the context of particular algorithms that use them for learning definite Horn formulas.Peer ReviewedPostprint (author's final draft
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Structure identification in relational data
This paper presents several investigations into the prospects for identifying meaningful structures in empirical data, namely, structures permitting effective organization of the data to meet requirements of future queries. We propose a general framework whereby the notion of identifiability is given a precise formal definition similar to that of learnability. Using this framework, we then explore if a tractable procedure exists for deciding whether a given relation is decomposable into a constraint network or a CNF theory with desirable topology and, if the answer is positive, identifying the desired decomposition. Finally, we address the problem of expressing a given relation as a Horn theory and, if this is impossible, finding the best k-Horn approximation to the given relation. We show that both problems can be solved in time polynomial in the length of the data
Higher-order Program Verification as Satisfiability Modulo Theories with Algebraic Data-types
We report on work in progress on automatic procedures for proving properties
of programs written in higher-order functional languages. Our approach encodes
higher-order programs directly as first-order SMT problems over Horn clauses.
It is straight-forward to reduce Hoare-style verification of first-order
programs into satisfiability of Horn clauses. The presence of closures offers
several challenges: relatively complete proof systems have to account for
closures; and in practice, the effectiveness of search procedures depend on
encoding strategies and capabilities of underlying solvers. We here use
algebraic data-types to encode closures and rely on solvers that support
algebraic data-types. The viability of the approach is examined using examples
from the literature on higher-order program verification
Synthesizing Modular Invariants for Synchronous Code
In this paper, we explore different techniques to synthesize modular
invariants for synchronous code encoded as Horn clauses. Modular invariants are
a set of formulas that characterizes the validity of predicates. They are very
useful for different aspects of analysis, synthesis, testing and program
transformation. We describe two techniques to generate modular invariants for
code written in the synchronous dataflow language Lustre. The first technique
directly encodes the synchronous code in a modular fashion. While in the second
technique, we synthesize modular invariants starting from a monolithic
invariant. Both techniques, take advantage of analysis techniques based on
property-directed reachability. We also describe a technique to minimize the
synthesized invariants.Comment: In Proceedings HCVS 2014, arXiv:1412.082
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