Unification and Logarithmic Space

We present an algebraic characterization of the complexity classes Logspace and NLogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is inspired from proof theory and more specifically linear logic and Geometry of Interaction. We show how unification can be used to build a model of computation by means of specific subalgebras associated to finite permutations groups. We then prove that whether an observation (the algebraic counterpart of a program) accepts a word can be decided within logarithmic space. We also show that the construction can naturally represent pointer machines, an intuitive way of understanding logarithmic space computing

On paths-based criteria for polynomial time complexity in proof-nets

Girard's Light linear logic (LLL) characterized polynomial time in the proof-as-program paradigm with a bound on cut elimination. This logic relied on a stratification principle and a "one-door" principle which were generalized later respectively in the systems L^4 and L^3a. Each system was brought with its own complex proof of Ptime soundness. In this paper we propose a broad sufficient criterion for Ptime soundness for linear logic subsystems, based on the study of paths inside the proof-nets, which factorizes proofs of soundness of existing systems and may be used for future systems. As an additional gain, our bound stands for any reduction strategy whereas most bounds in the literature only stand for a particular strategy.Comment: Long version of a conference pape

A feasible algorithm for typing in Elementary Affine Logic

We give a new type inference algorithm for typing lambda-terms in Elementary Affine Logic (EAL), which is motivated by applications to complexity and optimal reduction. Following previous references on this topic, the variant of EAL type system we consider (denoted EAL*) is a variant without sharing and without polymorphism. Our algorithm improves over the ones already known in that it offers a better complexity bound: if a simple type derivation for the term t is given our algorithm performs EAL* type inference in polynomial time.Comment: 20 page

Minimizing Test Power in SRAM through Reduction of Pre-charge Activity

In this paper we analyze the test power of SRAM memories and demonstrate that the full functional pre-charge activity is not necessary during test mode because of the predictable addressing sequence. We exploit this observation in order to minimize power dissipation during test by eliminating the unnecessary power consumption associated with the pre-charge activity. This is achieved through a modified pre-charge control circuitry, exploiting the first degree of freedom of March tests, which allows choosing a specific addressing sequence. The efficiency of the proposed solution is validated through extensive Spice simulations

Developments in Voltage Contrast

The aim of this paper is to give a review of the main steps that have led to voltage contrast equipment available to day for integrated circuit testing. The main parameters related to quantitative voltage evaluations are discussed in the case of measurements on integrated circuits metal stripes as well as on buried lines. They concern the reduction of the local field effects, the voltage resolution improvements on the energy analysers, and the time resolution. Results concerning the E-beam perturbation of MOS circuits are reported. Due to the test conditions and the presence of additional elements inside the microscope column limitations are introduced in spatial resolution. The performances available are given. They are consistent with today\u27s microelectronics. But, for the future, we show in this paper that the debate is not closed. It concerns both basic improvements and developments related to the use of the E-beam testers

A Logical Product Approach to Zonotope Intersection

We define and study a new abstract domain which is a fine-grained combination of zonotopes with polyhedric domains such as the interval, octagon, linear templates or polyhedron domain. While abstract transfer functions are still rather inexpensive and accurate even for interpreting non-linear computations, we are able to also interpret tests (i.e. intersections) efficiently. This fixes a known drawback of zonotopic methods, as used for reachability analysis for hybrid sys- tems as well as for invariant generation in abstract interpretation: intersection of zonotopes are not always zonotopes, and there is not even a best zonotopic over-approximation of the intersection. We describe some examples and an im- plementation of our method in the APRON library, and discuss some further in- teresting combinations of zonotopes with non-linear or non-convex domains such as quadratic templates and maxplus polyhedra

Logic Programming and Logarithmic Space

We present an algebraic view on logic programming, related to proof theory and more specifically linear logic and geometry of interaction. Within this construction, a characterization of logspace (deterministic and non-deterministic) computation is given via a synctactic restriction, using an encoding of words that derives from proof theory. We show that the acceptance of a word by an observation (the counterpart of a program in the encoding) can be decided within logarithmic space, by reducing this problem to the acyclicity of a graph. We show moreover that observations are as expressive as two-ways multi-heads finite automata, a kind of pointer machines that is a standard model of logarithmic space computation

Lazy Abstraction-Based Controller Synthesis

We present lazy abstraction-based controller synthesis (ABCS) for continuous-time nonlinear dynamical systems against reach-avoid and safety specifications. State-of-the-art multi-layered ABCS pre-computes multiple finite-state abstractions of varying granularity and applies reactive synthesis to the coarsest abstraction whenever feasible, but adaptively considers finer abstractions when necessary. Lazy ABCS improves this technique by constructing abstractions on demand. Our insight is that the abstract transition relation only needs to be locally computed for a small set of frontier states at the precision currently required by the synthesis algorithm. We show that lazy ABCS can significantly outperform previous multi-layered ABCS algorithms: on standard benchmarks, lazy ABCS is more than 4 times faster

Typing Quantum Superpositions and Measurement

We propose a way to unify two approaches of non-cloning in quantum lambda-calculi. The first approach is to forbid duplicating variables, while the second is to consider all lambda-terms as algebraic-linear functions. We illustrate this idea by defining a quantum extension of first-order simply-typed lambda-calculus, where the type is linear on superposition, while allows cloning base vectors. In addition, we provide an interpretation of the calculus where superposed types are interpreted as vector spaces and non-superposed types as their basis.Fil: Díaz Caro, Alejandro. Universidad Nacional de Quilmes. Departamento de Ciencia y Tecnología; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Dowek, Gilles. Institut National de Recherche en Informatique et en Automatique; Franci