A Framework to Synergize Partial Order Reduction with State Interpolation

We address the problem of reasoning about interleavings in safety verification of concurrent programs. In the literature, there are two prominent techniques for pruning the search space. First, there are well-investigated trace-based methods, collectively known as "Partial Order Reduction (POR)", which operate by weakening the concept of a trace by abstracting the total order of its transitions into a partial order. Second, there is state-based interpolation where a collection of formulas can be generalized by taking into account the property to be verified. Our main contribution is a framework that synergistically combines POR with state interpolation so that the sum is more than its parts

Backdoors to Normality for Disjunctive Logic Programs

Over the last two decades, propositional satisfiability (SAT) has become one of the most successful and widely applied techniques for the solution of NP-complete problems. The aim of this paper is to investigate theoretically how Sat can be utilized for the efficient solution of problems that are harder than NP or co-NP. In particular, we consider the fundamental reasoning problems in propositional disjunctive answer set programming (ASP), Brave Reasoning and Skeptical Reasoning, which ask whether a given atom is contained in at least one or in all answer sets, respectively. Both problems are located at the second level of the Polynomial Hierarchy and thus assumed to be harder than NP or co-NP. One cannot transform these two reasoning problems into SAT in polynomial time, unless the Polynomial Hierarchy collapses. We show that certain structural aspects of disjunctive logic programs can be utilized to break through this complexity barrier, using new techniques from Parameterized Complexity. In particular, we exhibit transformations from Brave and Skeptical Reasoning to SAT that run in time O(2^k n^2) where k is a structural parameter of the instance and n the input size. In other words, the reduction is fixed-parameter tractable for parameter k. As the parameter k we take the size of a smallest backdoor with respect to the class of normal (i.e., disjunction-free) programs. Such a backdoor is a set of atoms that when deleted makes the program normal. In consequence, the combinatorial explosion, which is expected when transforming a problem from the second level of the Polynomial Hierarchy to the first level, can now be confined to the parameter k, while the running time of the reduction is polynomial in the input size n, where the order of the polynomial is independent of k.Comment: A short version will appear in the Proceedings of the Proceedings of the 27th AAAI Conference on Artificial Intelligence (AAAI'13). A preliminary version of the paper was presented on the workshop Answer Set Programming and Other Computing Paradigms (ASPOCP 2012), 5th International Workshop, September 4, 2012, Budapest, Hungar

A Subsampling Line-Search Method with Second-Order Results

In many contemporary optimization problems such as those arising in machine learning, it can be computationally challenging or even infeasible to evaluate an entire function or its derivatives. This motivates the use of stochastic algorithms that sample problem data, which can jeopardize the guarantees obtained through classical globalization techniques in optimization such as a trust region or a line search. Using subsampled function values is particularly challenging for the latter strategy, which relies upon multiple evaluations. On top of that all, there has been an increasing interest for nonconvex formulations of data-related problems, such as training deep learning models. For such instances, one aims at developing methods that converge to second-order stationary points quickly, i.e., escape saddle points efficiently. This is particularly delicate to ensure when one only accesses subsampled approximations of the objective and its derivatives. In this paper, we describe a stochastic algorithm based on negative curvature and Newton-type directions that are computed for a subsampling model of the objective. A line-search technique is used to enforce suitable decrease for this model, and for a sufficiently large sample, a similar amount of reduction holds for the true objective. By using probabilistic reasoning, we can then obtain worst-case complexity guarantees for our framework, leading us to discuss appropriate notions of stationarity in a subsampling context. Our analysis encompasses the deterministic regime, and allows us to identify sampling requirements for second-order line-search paradigms. As we illustrate through real data experiments, these worst-case estimates need not be satisfied for our method to be competitive with first-order strategies in practice

Case-based maintenance : Structuring and incrementing the Case.

International audienceTo avoid performance degradation and maintain the quality of results obtained by the case-based reasoning (CBR) systems, maintenance becomes necessary, especially for those systems designed to operate over long periods and which must handle large numbers of cases. CBR systems cannot be preserved without scanning the case base. For this reason, the latter must undergo maintenance operations.The techniques of case base’s dimension optimization is the analog of instance reduction size methodology (in the machine learning community). This study links these techniques by presenting case-based maintenance in the framework of instance based reduction, and provides: first an overview of CBM studies, second, a novel method of structuring and updating the case base and finally an application of industrial case is presented.The structuring combines a categorization algorithm with a measure of competence CM based on competence and performance criteria. Since the case base must progress over time through the addition of new cases, an auto-increment algorithm is installed in order to dynamically ensure the structuring and the quality of a case base. The proposed method was evaluated through a case base from an industrial plant. In addition, an experimental study of the competence and the performance was undertaken on reference benchmarks. This study showed that the proposed method gives better results than the best methods currently found in the literature

Anytime Computation of Cautious Consequences in Answer Set Programming

Query answering in Answer Set Programming (ASP) is usually solved by computing (a subset of) the cautious consequences of a logic program. This task is computationally very hard, and there are programs for which computing cautious consequences is not viable in reasonable time. However, current ASP solvers produce the (whole) set of cautious consequences only at the end of their computation. This paper reports on strategies for computing cautious consequences, also introducing anytime algorithms able to produce sound answers during the computation.Comment: To appear in Theory and Practice of Logic Programmin

Constraining Montague Grammar for computational applications

This work develops efficient methods for the implementation of Montague Grammar on a computer. It covers both the syntactic and the semantic aspects of that task. Using a simplified but adequate version of Montague Grammar it is shown how to translate from an English fragment to a purely extensional first-order language which can then be made amenable to standard automatic theorem-proving techniques. Translating a sentence of Montague English into the first-order predicate calculus usually proceeds via an intermediate translation in the typed lambda calculus which is then simplified by lambda-reduction to obtain a first-order equivalent. If sufficient sortal structure underlies the type theory for the reduced translation to always be a first-order one then perhaps it should be directly constructed during the syntactic analysis of the sentence so that the lambda-expressions never come into existence and no further processing is necessary. A method is proposed to achieve this involving the unification of meta-logical expressions which flesh out the type symbols of Montague's type theory with first-order schemas. It is then shown how to implement Montague Semantics without using a theorem prover for type theory. Nothing more than a theorem prover for the first-order predicate calculus is required. The first-order system can be used directly without encoding the whole of type theory. It is only necessary to encode a part of second-order logic and this can be done in an efficient, succinct, and readable manner. Furthermore the pseudo-second-order terms need never appear in any translations provided by the parser. They are vital just when higher-order reasoning must be simulated. The foundation of this approach is its five-sorted theory of Montague Semantics. The objects in this theory are entities, indices, propositions, properties, and quantities. It is a theory which can be expressed in the language of first-order logic by means of axiom schemas and there is a finite second-order axiomatisation which is the basis for the theorem-proving arrangement. It can be viewed as a very constrained set theory