Related papers: A Prime Decomposition of Probabilistic Automata
Deciding formulas mixing arithmetic and uninterpreted predicates is of practical interest, notably for applications in verification. Some decision procedures consist in building by structural induction an automaton that recognizes the set…
We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of…
Developing robust representations of chemical structures that enable models to learn topological inductive biases is challenging. In this manuscript, we present a representation of atomistic systems. We begin by proving that our…
Underwater robotics addresses the problem of object detection apparatus. Offers a probabilistic formulation of the problem, which uses the reduction of the detection task to a classical task of Buffon. This formulation arises naturally in…
We introduce a notion of the ``explanation" of one (generalized) probabilistic model by another as particular kind of span in the category $\Prob$ of probabilistic models and morphisms. We show that explanations compose under a standard…
It is undecidable whether the language recognized by a probabilistic finite automaton is empty. Several other undecidability results, in particular regarding problems about matrix products, are based on this important theorem. We present…
In this work, we study the fully automated inference of expected result values of probabilistic programs in the presence of natural programming constructs such as procedures, local variables and recursion. While crucial, capturing these…
A deterministic finite automaton (DFA) is composite if its language can be decomposed into an intersection of languages of smaller DFAs. Otherwise, A is prime. This notion of primality was introduced by Kupferman and Mosheiff in 2013, and…
We study automaton structures, i.e. groups, monoids and semigroups generated by an automaton, which, in this context, means a deterministic finite-state letter-to-letter transducer. Instead of considering only complete automata, we…
We show that a special case of the Feferman-Vaught composition theorem gives rise to a natural notion of automata for finite words over an infinite alphabet, with good closure and decidability properties, as well as several logical…
Finite automata are used to encode geometric figures, functions and can be used for image compression and processing. The original approach is to represent each point of a figure in $\mathbb{R}^n$ as a convolution of its $n$ coordinates…
We consider probabilistic automata on a general state space and study their computational power. The model is based on the concept of language recognition by probabilistic automata due to Rabin and models of analog computation in a noisy…
A deterministic finite (semi)automaton is primitive if its transition monoid (semigroup) acting on the set of states has no non-trivial congruences. It is synchronizing if it contains a constant map (transformation). In analogy to…
We present an effective method for computing parametric primary decomposition via comprehensive Gr\"obner systems. In general, it is very difficult to compute a parametric primary decomposition of a given ideal in the polynomial ring with…
Over any partially ordered abelian group whose positive cone is closed in an appropriate sense and has finitely many faces, modules that satisfy a weak finiteness condition admit finite primary decompositions. This conclusion rests on the…
We establish an assume-guarantee (AG) framework for compositional reasoning about multi-objective queries in parametric probabilistic automata (pPA) - an extension to probabilistic automata (PA), where transition probabilities are functions…
To study relationship between quantum finite automata and probabilistic finite automata, we introduce a notion of probabilistic reversible automata (PRA, or doubly stochastic automata). We find that there is a strong relationship between…
The upper estimate of the percolation threshold of the Bernoulli random field on the hexagonal lattice is found. It is done on the basis of the cluster decomposition. Each term of the decomposition is estimated using the number estimate of…
The notion of probability plays an important role in almost all areas of science and technology. In modern mathematics, however, probability theory means nothing other than measure theory, and the operational characterization of the notion…
We model stochastic choices with categorization. The agent preliminarly groups alternatives in homogenous disjoint classes, then randomly chooses one class and randomly picks an item within the selected class. We give a formal definition of…