Enforcing Termination of Interprocedural Analysis

Interprocedural analysis by means of partial tabulation of summary functions may not terminate when the same procedure is analyzed for infinitely many abstract calling contexts or when the abstract domain has infinite strictly ascending chains. As a remedy, we present a novel local solver for general abstract equation systems, be they monotonic or not, and prove that this solver fails to terminate only when infinitely many variables are encountered. We clarify in which sense the computed results are sound. Moreover, we show that interprocedural analysis performed by this novel local solver, is guaranteed to terminate for all non-recursive programs --- irrespective of whether the complete lattice is infinite or has infinite strictly ascending or descending chains

Efficient Groundness Analysis in Prolog

Boolean functions can be used to express the groundness of, and trace grounding dependencies between, program variables in (constraint) logic programs. In this paper, a variety of issues pertaining to the efficient Prolog implementation of groundness analysis are investigated, focusing on the domain of definite Boolean functions, Def. The systematic design of the representation of an abstract domain is discussed in relation to its impact on the algorithmic complexity of the domain operations; the most frequently called operations should be the most lightweight. This methodology is applied to Def, resulting in a new representation, together with new algorithms for its domain operations utilising previously unexploited properties of Def -- for instance, quadratic-time entailment checking. The iteration strategy driving the analysis is also discussed and a simple, but very effective, optimisation of induced magic is described. The analysis can be implemented straightforwardly in Prolog and the use of a non-ground representation results in an efficient, scalable tool which does not require widening to be invoked, even on the largest benchmarks. An extensive experimental evaluation is givenComment: 31 pages To appear in Theory and Practice of Logic Programmin

Statistical mechanics of lossy data compression using a non-monotonic perceptron

The performance of a lossy data compression scheme for uniformly biased Boolean messages is investigated via methods of statistical mechanics. Inspired by a formal similarity to the storage capacity problem in the research of neural networks, we utilize a perceptron of which the transfer function is appropriately designed in order to compress and decode the messages. Employing the replica method, we analytically show that our scheme can achieve the optimal performance known in the framework of lossy compression in most cases when the code length becomes infinity. The validity of the obtained results is numerically confirmed.Comment: 9 pages, 5 figures, Physical Review