Related papers: A Prime Decomposition of Probabilistic Automata
We consider blind, deterministic, finite automata equipped with a register which stores an element of a given monoid, and which is modified by right multiplication by monoid elements. We show that, for monoids M drawn from a large class…
We introduce a logic to express structural properties of automata with string inputs and, possibly, outputs in some monoid. In this logic, the set of predicates talking about the output values is parametric, and we provide sufficient…
This paper introduces and studies the sequential composition and decomposition of propositional logic programs. We show that acyclic programs can be decomposed into single-rule programs and provide a general decomposition result for…
This paper is concerned with the primitive cohomology of a smooth projective hypersurface considered as a linear representation for its automorphism group. Using the Lefschetz-Riemann-Roch formula, the character of this representation is…
The results of the study provide guidelines for the development and applications of algorithms. When the number of steps for calculating an assumption tends to infinity, probability theory can be applied to predict whether the assumption…
Primary decomposition of commutative monoid congruences is insensitive to certain features of primary decomposition in commutative rings. These features are captured by the more refined theory of mesoprimary decomposition of congruences,…
It is shown that the proton formation probability, extracted from experimental data corresponding to one-proton radioactivity, is divided into two regions when plotted as a function of an universal parameter. This parameter is derived from…
Self-organizing complex systems can be modeled using cellular automaton models. However, the parametrization of these models is crucial and significantly determines the resulting structural pattern. In this research, we introduce and…
In this paper, we consider the probability that a randomly chosen automorphism of a finite group fixes a randomly chosen element of a subgroup of that group. We obtain several new results as well as generalizations and improvements of some…
Probabilistic abstract interpretation is a theory used to extract particular properties of a computer program when it is infeasible to test every single inputs. In this paper we apply the theory on neural networks for the same purpose: to…
A stochastic timed automaton is a purely stochastic process defined on a timed automaton, in which both delays and discrete choices are made randomly. We study the almost-sure model-checking problem for this model, that is, given a…
In this paper we introduce a new quantum computation model, the linear quantum cellular automaton. Well-formedness is an essential property for any quantum computing device since it enables us to define the probability of a configuration in…
We state a conjecture on the reduction modulo the defining characteristic of a unipotent representation of a finite reductive group.
Aspects of the theory of characteristic modes, based on their variational formulation, are presented and an explicit form of a related functional, involving only currents in a spatial domain, is derived. The new formulation leads to deeper…
Automorphism-ensemble decoding is applied to the Plotkin constituents of Reed-Muller codes, resulting in a new soft-decision decoding algorithm with state-of-the-art performance versus complexity trade-offs.
We introduce hypernode automata as a new specification formalism for hyperproperties of concurrent systems. They are finite automata with nodes labeled with hypernode logic formulas and transitions labeled with actions. A hypernode logic…
Automatic groups admitting prefix closed automatic structures with uniqueness are characterized as the quotients of free groups by normal subgroups possessing sets of free generators satisfying certain language-theoretic conditions.
We study natural linear representations of self-similar groups over finite fields. In particular, we show that if the group is generated by a finite automaton, then obtained matrices are automatic. This shows a new relation between two…
Consider $ A^* $, the free monoid generated by the finite alphabet $A$ with the concatenation operation. Two words have the same commutative image when one is a permutation of the symbols of the other. The commutative closure of a set $ L…
In this paper we study primality and primary decomposition of certain ideals which are generated by homogeneous degree $2$ polynomials and occur naturally from determinantal conditions. Normality is derived from these results.