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Nondeterministic automata may be viewed as succinct programs implementing deterministic automata, i.e. complete specifications. Converting a given deterministic automaton into a small nondeterministic one is known to be computationally very…
As machine learning applications grow increasingly ubiquitous and complex, they face an increasing set of requirements beyond accuracy. The prevalent approach to handle this challenge is to aggregate a weighted combination of requirement…
In this paper we investigate careful synchronization of one-cluster partial automata. First we prove that in general case the shortest carefully synchronizing word for such automata is of length $2^\frac{n}{2} + 1$, where $n$ is the number…
We introduce the notion of adaptive synchronisation for pushdown automata, in which there is an external observer who has no knowledge about the current state of the pushdown automaton, but can observe the contents of the stack. The…
Cellular automata are one-dimensional arrays of interconnected interacting finite automata. We investigate one of the weakest classes, the real-time one-way cellular automata, and impose an additional restriction on their inter-cell…
We survey recent results concerning the complexity of regular languages represented by their minimal deterministic finite automata. In addition to the quotient complexity of the language -- which is the number of its (left) quotients, and…
We consider probabilistic automata on infinite words with acceptance defined by parity conditions. We consider three qualitative decision problems: (i) the positive decision problem asks whether there is a word that is accepted with…
We study the verification of distributed systems where processes are finite automata with access to a shared pool of locks. We consider objectives that are boolean combinations of local regular constraints. We show that the problem,…
Many researchers in artificial intelligence are beginning to explore the use of soft constraints to express a set of (possibly conflicting) problem requirements. A soft constraint is a function defined on a collection of variables which…
Shared resources synchronization is a well studied problem, in both shared memory environment or distributed memory environment. Many synchronization mechanisms are proposed, with their own way to reach certain consistency level. This…
Known sparsity thresholds for basis pursuit to deliver the maximally sparse solution of the compressed sensing recovery problem typically depend on the dictionary's coherence. While the coherence is easy to compute, it can lead to rather…
We investigate the intersection problem for finite monoids, which asks for a given set of regular languages, represented by recognizing morphisms to finite monoids from a variety V, whether there exists a word contained in their…
Separation is a classical problem asking whether, given two sets belonging to some class, it is possible to separate them by a set from a smaller class. We discuss the separation problem for regular languages. We give a Ptime algorithm to…
Regular synchronization languages can be used to define rational relations of finite words, and to characterize subclasses of rational relations, like automatic or recognizable relations. We provide a systematic study of the decidability of…
Fast matching of regular expressions with bounded repetition, aka counting, such as (ab){50,100}, i.e., matching linear in the length of the text and independent of the repetition bounds, has been an open problem for at least two decades.…
Constraint automata are an adaptation of B\"uchi-automata that process data words where the data comes from some relational structure S. Every transition of such an automaton comes with constraints in terms of the relations of S. A…
A condition characterizing the class of regular languages which have several nonisomorphic minimal reversible automata is presented. The condition concerns the structure of the minimum automaton accepting the language under consideration.…
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…
Typestate systems ensure many desirable properties of imperative programs, including initialization of object fields and correct use of stateful library interfaces. Abstract sets with cardinality constraints naturally generalize typestate…
Indexed languages are a classical notion in formal language theory, which has attracted attention in recent decades due to its role in higher-order model checking: They are precisely the languages accepted by order-2 pushdown automata. The…