Related papers: A Prime Decomposition of Probabilistic Automata
We study primary submodules and primary decompositions from a differential and computational point of view. Our main theoretical contribution is a general structure theory and a representation theorem for primary submodules of an arbitrary…
The automaticity $A(x)$ of a set $\mathcal{X}$ is the size of the smallest automaton that recognizes $\mathcal{X}$ on all words of length $\leq x$. We show that the automaticity of the set of primes is at least $x\exp\left(-c(\log\log…
In combinatorics, the probabilistic method is a very powerful tool to prove the existence of combinatorial objects with interesting and useful properties. Explicit constructions of objects with such properties are often very difficult, or…
Decomposable models and Bayesian networks can be defined as sequences of oligo-dimensional probability measures connected with operators of composition. The preliminary results suggest that the probabilistic models allowing for effective…
In this paper we present two interesting properties of stochastic cellular automata that can be helpful in analyzing the dynamical behavior of such automata. The first property allows for calculating cell-wise probability distributions over…
An a priori semimeasure (also known as "algorithmic probability" or "the Solomonoff prior" in the context of inductive inference) is defined as the transformation, by a given universal monotone Turing machine, of the uniform measure on the…
Under the name prime decomposition (pd), a unique decomposition of an arbitrary $N$-dimensional density matrix $\rho$ into a sum of seperable density matrices with dimensions given by the coprime factors of $N$ is introduced. For a class of…
Probabilistic timed automata are classical timed automata extended with discrete probability distributions over edges. We introduce clock-dependent probabilistic timed automata, a variant of probabilistic timed automata in which transition…
Machine learning models that predict the feasibility of chemical reactions have become central to automated synthesis planning. Despite their predictive success, these models often lack transparency and interpretability. We introduce a…
Most ideas about what an algorithm is are very similar. Basic operations are used for transforming objects. The evaluation of internal and external states by relations has impact on the further process. A more precise definition can lead to…
In this paper we characterize the congruence associated to the direct sum of all irreducible representations of a finite semigroup over an arbitrary field, generalizing results of Rhodes for the field of complex numbers. Applications are…
We study languages over infinite alphabets equipped with some structure that can be tested by recognizing automata. We develop a framework for studying such alphabets and the ensuing automata theory, where the key role is played by an…
Abstracting an effective theory from a complicated process is central to the study of complexity. Even when the underlying mechanisms are understood, or at least measurable, the presence of dissipation and irreversibility in biological,…
Automata over infinite words, also known as omega-automata, play a key role in the verification and synthesis of reactive systems. The spectrum of omega-automata is defined by two characteristics: the acceptance condition (e.g. B\"uchi or…
We study a family of determinantal ideals whose decompositions encode the structural zeros in conditional independence models with hidden variables. We provide explicit decompositions of these ideals and, for certain subclasses of models,…
Probabilistic programs encode stochastic models as ordinary-looking programs with primitives for sampling numbers from predefined distributions and conditioning. Their applications include, among many others, machine learning and modeling…
Primary decomposition is a very important tool of commutative algebra and geometry. In this paper we generalized some of the existing algorithms of primary decomposition developed by Eisenbud et al. (cf. [EHV]) for free modules and also…
Soliton automata are mathematical models of soliton switching in chemical molecules. Several concepts of determinism for soliton automata have been defined. The concept of strong determinism has been investigated for the case in which only…
We examine properties of generic automorphisms of the random poset, with the goal of explicitly characterizing them. We associate to each automorphism an auxiliary first-order structure, consisting of the random poset equipped with an…
Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…