This paper describes the integration of an LP solver into iSAT, a Satisfiability Modulo Theories solver that can solve Boolean combinations of linear and nonlinear constraints. iSAT is a tight integration of the well-known DPLL algorithm and interval constraint propagation allowing it to reason about linear and nonlinear constraints. As interval arithmetic is known to be less efficient on solvi...

We consider Presburger arithmetic (PA) extended with modulo counting quantifiers. We show that its complexity is essentially the same as that of PA, i.e., we give a doubly exponential space bound. This is done by giving and analysing a quantifier elimination procedure similar to Reddy and Loveland’s procedure for PA. We also show that the complexity of the automata-based decision procedure for ...

We present a general uni cation algorithm modulo Presburger Arithmetic for a restricted class of modularly speci ed theories where function symbols of the target theory have non arithmetic codomain sorts. Additionally, we comment on conditions guaranteeing decidability of matching and uni cation problems modulo more general theories than the arithmetic ones, which appear when automated deductio...

Redundancy is de ned as the excess of the code length over the optimal (ideal) code length. We study the average redundancy of an idealized arithmetic coding (for memoryless sources with unknown distributions) in which the Krichevsky and Tro mov estimator is followed by the Shannon{Fano code. We shall ignore here important practical implementation issues such as nite precisions and nite bu er s...

For a polynomial f ∈ Fp[X], we obtain an upper bound on the number of points (x, f(x)) modulo a prime p which belong to an arbitrary square with the side length H. Our results is based on the Vinogradov mean value theorem. Using these estimates we obtain results on the expansion of orbits in dynamical systems generated by nonlinear polynomials and we obtain an asymptotic formula for the number ...

We investigate the energy efficiency of interspike interval (ISI) neural codes. Using the hypothesis that nature maximizes the energy efficiency of information processing, it is possible to derive neuronal firing frequencies which maximize the information/energy ratio. With simple assumptions about the encoded ISI and noise distributions, we show that ISI codes can be at least as efficient as d...

The problem of designing robust controller for discrete two-time-scale interval systems, conveniently represented using interval matrix notion, is considered. The original full order twotime-scale interval system is decomposed into slow and fast subsystems using interval arithmetic. The controllers designed independently to stabilize these two subsystems are combined to get a composite controll...

Finite Lorentz groups acting on 4-dimensional vector spaces coordinatized by finite fields with a prime number of elements are represented as homomorphic images of countable, rational subgroups of the Lorentz group acting on real 4-dimensional space-time. Bounded subsets of the real Lorentz group are retractable with arbitrary precision to finite subsets of such rational subgroups. These finite...

We provide a detailed analysis of Kahan’s algorithm for the accurate computation of the determinant of a 2 × 2 matrix. This algorithm requires the availability of a fused multiply-add instruction. Assuming radix-β, precision-p floating-point arithmetic with β even, p ≥ 2, and barring overflow or underflow we show that the absolute error of Kahan’s algorithm is bounded by (β+1)/2 ulps of the exa...

We study here the algorithmic analysis of systems modeled in terms of availability languages. Our first main result is a positive answer to the emptiness problem: it is decidable whether a given availability language contains a word. The key idea is an inductive construction that replaces availability languages with Parikh-equivalent regular languages. As a second contribution, we solve the int...