Related papers: A Prime Decomposition of Probabilistic Automata

Since the 1970s with the work of McNaughton, Papert and Sch\"utzenberger, a regular language is known to be definable in the first-order logic if and only if its syntactic monoid is aperiodic. This algebraic characterisation of a…

Algorithms which learn environments represented by automata in the past have had complexity scaling with the number of states in the automaton, which can be exponentially large even for automata recognizing regular expressions with a small…

The generation of comprehensible explanations is an essential feature of modern artificial intelligence systems. In this work, we consider probabilistic logic programming, an extension of logic programming which can be useful to model…

A theorem is derived which determines higher order first integrals of autonomous holonomic dynamical systems in a general space, provided the collineations and the Killing tensors -- up to the order of the first integral -- of the kinetic…

Computational mechanics, an approach to structural complexity, defines a process's causal states and gives a procedure for finding them. We show that the causal-state representation--an $\epsilon$-machine--is the minimal one consistent with…

For a given discrete decomposable graphical model, we identify several alternative parametrizations, and construct the corresponding reference priors for suitable groupings of the parameters. Specifically, assuming that the cliques of the…

We classify the homogeneous finite-dimensional permutation structures, i.e., homogeneous structures in a language of finitely many linear orders, giving a nearly complete answer to a question of Cameron, and confirming the classification…

We generalize some of the central results in automata theory to the abstraction level of coalgebras and thus lay out the foundations of a universal theory of automata operating on infinite objects. Let F be any set functor that preserves…

This paper develops an assume-guarantee (AG) framework for the compositional verification of probabilistic automata (PAs) with uncertain transition probabilities. We study parametric probabilistic automata (pPAs), where probabilities are…

We are now witnessing a rapid growth of a new part of group theory which has become known as "statistical group theory". A typical result in this area would say something like ``a random element (or a tuple of elements) of a group G has a…

In the paper we develop the $p$-adic theory of discrete automata. Every automaton $\mathfrak A$ (transducer) whose input/output alphabets consist of $p$ symbols can be associated to a continuous (in fact, 1-Lipschitz) map from $p$-adic…

Machine learning (ML) has emerged as a powerful tool for tackling complex regression and classification tasks, yet its success often hinges on the quality of training data. This study introduces an ML paradigm inspired by domain knowledge…

We determine the representation of the group of automorphisms for cyclotomic function fields in characteristic $p > 0$ induced by the natural action on the space of holomorphic differentials via construction of an explicit basis of…

This paper introduces and investigates decision problems for numberless probabilistic automata, i.e. probabilistic automata where the support of each probabilistic transitions is specified, but the exact values of the probabilities are not.…

The random permutation is the Fra\"iss\'e limit of the class of finite structures with two linear orders. Answering a problem stated by Peter Cameron in 2002, we use a recent Ramsey-theoretic technique to show that there exist precisely 39…

The state complexity of a Deterministic Finite-state automaton (DFA) is the number of states in its minimal equivalent DFA. We study the state complexity of random $n$-state DFAs over a $k$-symbol alphabet, drawn uniformly from the set…

Neural networks are becoming a popular tool for solving many real-world problems such as object recognition and machine translation, thanks to its exceptional performance as an end-to-end solution. However, neural networks are complex…

We present a mechanism for constructing graphical models, specifically Bayesian networks, from a knowledge base of general probabilistic information. The unique feature of our approach is that it uses a powerful first-order probabilistic…

In this paper we establish an abstraction of on-the-fly determinization of finite-state automata using transition monoids and demonstrate how it can be applied to bound the asymptotics. We present algebraic and combinatorial properties that…

We discuss a characterization of complexity based on successive approximations of the probability density describing a system by means of maximum entropy methods, thereby quantifying the respective role played by different orders of…