We investigate the computational power of continuous-time neural networks with Hoppeld-type units. We prove that polynomial-size networks with saturated-linear response functions are at least as powerful as polynomially space-bounded Turing machines.

It is shown by means of Markov c hain analysis that unimodal binary long path problems can be solved by m utation and elitist selection in a polynomially bounded number of trials on average.

We investigate upper bounds on the sample-size sufficient for ‘solid’ learnability with respect to a probability distribution. We obtain a sufficient condition for feasible (polynomially bounded) sample-size bounds for distributionspecific (solid) learnability.

Let R be an o-minimal expansion of a real closed field. We show that the definable infinitely Peano differentiable functions are smooth if and only if R is polynomially bounded.

Abstract We use a Voronoi-type tessellation based on compound Poisson point process to construct polynomially mixing stationary random smooth planar vector field with bounded nonnegative components such that, probability one, none of the associated integral curves possess an asymptotic direction.

We prove that the class of context-free languages with polynomially bounded ambiguity (PCFL) is the closure of the class of unambiguous languages (UCFL) under projections which deletes Parikh bounded symbols only. A symbol a is Parikh bounded in a language L if there is a constant c such that no word of L contains more than c occurrences of a. Furthermore PCFL is closed under the formally stron...

It is shown that the discount factor needed to solve an undiscounted mean payoff stochastic game to optimality is exponentially close to 1, even in games with a single random node and polynomially bounded rewards and transition probabilities.

Real time constraints on AI systems require guaranteeing bounds on these systems’ performance. However, in the presence of sources of uncontrolled combinatorics, it is extremely difficult to guarantee such bounds on their performance. In production systems, the .prirnary source of uncontrolled combinatorics is the production match. To eliminate these combinatorics, the unique-attribute formulat...

We investigate the asymptotic behavior at +∞ of non-oscillatory solutions to differential equations y′ = G(t, y), t > a, where G : R1+l → Rl is definable in a polynomially bounded o-minimal structure. In particular, we show that the Pfaffian closure of a polynomially bounded o-minimal structure on the real field is levelled. A classical topic in asymptotic analysis is the study of the behavior ...