A Novel Basis for Logic Rewriting

Given a set of logic primitives and a Boolean function, exact synthesis finds the optimum representation (e.g., depth or size) of the function in terms of the primitives. Due to its high computational complexity, the use of exact synthesis is limited to small networks. Some logic rewriting algorithms use exact synthesis to replace small subnetworks by their optimum representations. However, conventional approaches have two major drawbacks. First, their scalability is limited, as Boolean functions are enumerated to precompute their optimum representations. Second, the strategies used to replace subnetworks are not satisfactory. We show how the use of exact synthesis for logic rewriting can be improved. To this end, we propose a novel method that includes various improvements over conventional approaches: (i) we improve the subnetwork selection strategy, (ii) we show how enumeration can be avoided, allowing our method to scale to larger subnetworks, and (iii) we introduce XOR Majority Graphs (XMGs) as compact logic representations that make exact synthesis more efficient. We show a 45.8% geometric mean reduction (taken over size, depth, and switching activity), a 6.5% size reduction, and depth · size reductions of 8.6%, compared to the academic state-of-the-art. Finally, we outperform 3 over 9 of the best known size results for the EPFL benchmark suite, reducing size by up to 11.5% and depth up to 46.7%

Singular and Plural Functions for Functional Logic Programming

Functional logic programming (FLP) languages use non-terminating and non-confluent constructor systems (CS's) as programs in order to define non-strict non-determi-nistic functions. Two semantic alternatives have been usually considered for parameter passing with this kind of functions: call-time choice and run-time choice. While the former is the standard choice of modern FLP languages, the latter lacks some properties---mainly compositionality---that have prevented its use in practical FLP systems. Traditionally it has been considered that call-time choice induces a singular denotational semantics, while run-time choice induces a plural semantics. We have discovered that this latter identification is wrong when pattern matching is involved, and thus we propose two novel compositional plural semantics for CS's that are different from run-time choice. We study the basic properties of our plural semantics---compositionality, polarity, monotonicity for substitutions, and a restricted form of the bubbling property for constructor systems---and the relation between them and to previous proposals, concluding that these semantics form a hierarchy in the sense of set inclusion of the set of computed values. We have also identified a class of programs characterized by a syntactic criterion for which the proposed plural semantics behave the same, and a program transformation that can be used to simulate one of them by term rewriting. At the practical level, we study how to use the expressive capabilities of these semantics for improving the declarative flavour of programs. We also propose a language which combines call-time choice and our plural semantics, that we have implemented in Maude. The resulting interpreter is employed to test several significant examples showing the capabilities of the combined semantics. To appear in Theory and Practice of Logic Programming (TPLP)Comment: 53 pages, 5 figure

A Strategy Language for Testing Register Transfer Level Logic

The development of modern ICs requires a huge investment in RTL verification. This is a reflection of brisk release schedules and the complexity of contemporary chip designs. A major bottleneck to reaching verification closure in such designs is the disproportionate effort expended in crafting directed tests; which is necessary to reach those behaviors that other, more automated testing methods fail to cover. This paper defines a novel language that can be used to generate targeted stimuli for RTL logic and which mitigates the complexities of writing directed tests. The main idea is to treat directed testing as a meta-reasoning problem about simulation. Our language is both formalized and prototyped as a proof-search strategy language in rewriting logic. We illustrate its novel features and practical use with several examples.published or submitted for publicatio

Structural Resolution with Co-inductive Loop Detection

A way to combine co-SLD style loop detection with structural resolution was found and is introduced in this work, to extend structural resolution with co-induction. In particular, we present the operational semantics, called co-inductive structural resolution, of this novel combination and prove its soundness with respect to the greatest complete Herbrand model.Comment: In Proceedings CoALP-Ty'16, arXiv:1709.0419

COSMICAH 2005: workshop on verification of COncurrent Systems with dynaMIC Allocated Heaps (a Satellite event of ICALP 2005) - Informal Proceedings

Lisboa Portugal, 10 July 200

Techniques for the Synthesis of Reversible Toffoli Networks

This paper presents novel techniques for the synthesis of reversible networks of Toffoli gates, as well as improvements to previous methods. Gate count and technology oriented cost metrics are used. Our synthesis techniques are independent of the cost metrics. Two new iterative synthesis procedure employing Reed-Muller spectra are introduced and shown to complement earlier synthesis approaches. The template simplification suggested in earlier work is enhanced through introduction of a faster and more efficient template application algorithm, updated (shorter) classification of the templates, and presentation of the new templates of sizes 7 and 9. A novel ``resynthesis'' approach is introduced wherein a sequence of gates is chosen from a network, and the reversible specification it realizes is resynthesized as an independent problem in hopes of reducing the network cost. Empirical results are presented to show that the methods are effective both in terms of the realization of all 3x3 reversible functions and larger reversible benchmark specifications.Comment: 20 pages, 5 figure

Rule Algebras for Adhesive Categories

We demonstrate that the most well-known approach to rewriting graphical structures, the Double-Pushout (DPO) approach, possesses a notion of sequential compositions of rules along an overlap that is associative in a natural sense. Notably, our results hold in the general setting of $\mathcal{M}$-adhesive categories. This observation complements the classical Concurrency Theorem of DPO rewriting. We then proceed to define rule algebras in both settings, where the most general categories permissible are the finitary (or finitary restrictions of) $\mathcal{M}$-adhesive categories with $\mathcal{M}$-effective unions. If in addition a given such category possess an $\mathcal{M}$-initial object, the resulting rule algebra is unital (in addition to being associative). We demonstrate that in this setting a canonical representation of the rule algebras is obtainable, which opens the possibility of applying the concept to define and compute the evolution of statistical moments of observables in stochastic DPO rewriting systems