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The problem of learning a minimal consistent model from a set of labeled sequences of symbols is addressed from a satisfiability modulo theories perspective. We present two encodings for deterministic finite automata and extend one of these…
Weighted automata is a basic tool for specification in quantitative verification, which allows to express quantitative features of analysed systems such as resource consumption. Quantitative specification can be assisted by automata…
Unambiguous non-deterministic finite automata have intermediate expressive power and succinctness between deterministic and non-deterministic automata. It has been conjectured that every unambiguous non-deterministic one-way finite…
We cast new light on the existing models of one-way deterministic topological automata by introducing a fresh but general, convenient model, in which, as each input symbol is read, an interior system of an automaton, known as a…
This paper considers finite-automata based algorithms for handling linear arithmetic with both real and integer variables. Previous work has shown that this theory can be dealt with by using finite automata on infinite words, but this…
Generalizations of linear numeration systems in which the set of natural numbers is recognizable by finite automata are obtained by describing an arbitrary infinite regular language following the lexicographic ordering. For these systems of…
Determinization of fuzzy finite automata is understood here as a procedure of their conversion into equivalent crisp-deterministic fuzzy automata, which can be viewed as being deterministic with possibly infinitely many states, but with…
Machine learning algorithms use error function minimization to fit a large set of parameters in a preexisting model. However, error minimization eventually leads to a memorization of the training dataset, losing the ability to generalize to…
The RPNI algorithm (Oncina, Garcia 1992) constructs deterministic finite automata from finite sets of negative and positive example words. We propose and analyze an extension of this algorithm to deterministic $\omega$-automata with…
Canonical is a solver for type inhabitation in dependent type theory, that is, the problem of producing a term of a given type. We present a Lean tactic which invokes Canonical to generate proof terms and synthesize programs. The tactic…
Limit-average automata are weighted automata on infinite words that use average to aggregate the weights seen in infinite runs. We study approximate learning problems for limit-average automata in two settings: passive and active. In the…
Statistics and Optimization are foundational to modern Machine Learning. Here, we propose an alternative foundation based on Abstract Algebra, with mathematics that facilitates the analysis of learning. In this approach, the goal of the…
We extend the L* algorithm to learn bimonoids recognising pomset languages. We then identify a class of pomset automata that accepts precisely the class of pomset languages recognised by bimonoids and show how to convert between bimonoids…
The study of finite automata and regular languages is a privileged meeting point of algebra and logic. Since the work of Buchi, regular languages have been classified according to their descriptive complexity, i.e. the type of logical…
Quantitative automata are useful representations for numerous applications, including modeling probability distributions over sequences to Markov chains and reward machines. Actively learning such automata typically occurs using explicitly…
Calibrated probabilistic classifiers are models whose predicted probabilities can directly be interpreted as uncertainty estimates. It has been shown recently that deep neural networks are poorly calibrated and tend to output overconfident…
We propose a query learning algorithm for residual symbolic finite automata (RSFAs). Symbolic finite automata (SFAs) are finite automata whose transitions are labeled by predicates over a Boolean algebra, in which a big collection of…
We propose an efficient algorithm for determinising counting automata (CAs), i.e., finite automata extended with bounded counters. The algorithm avoids unfolding counters into control states, unlike the na\"ive approach, and thus produces…
A two-way deterministic finite state automaton with one counter (2D1CA) is a fundamental computational model that has been examined in many different aspects since sixties, but we know little about its power in the case of unary languages.…
It is known that 2-state binary and 3-state unary probabilistic finite automata and 2-state unary quantum finite automata recognize uncountably many languages with cutpoints. These results have been obtained by associating each recognized…