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Compact representations of automata are important for efficiency. In this paper, we study methods to compute reduced automata, in which no two states accept the same language. We do this for finitary automata (FA), an abstract definition…
We give a new simple proof of the decidability of the First Order Theory of (omega^omega^i,+) and the Monadic Second Order Theory of (omega^i,<), improving the complexity in both cases. Our algorithm is based on tree automata and a new…
We present an extension of the Angluin-style learning algorithm for tree automata that incorporates deductive inference. The learning algorithm is provided with a term rewriting system that specifies properties of the target tree language…
Information, stored or transmitted in digital form, is often structured. Individual data records are usually represented as hierarchies of their elements. Together, records form larger structures. Information processing applications have to…
The theory of finite automata concerns itself with words in a free monoid together with concatenation and without further structure. There are, however, important applications which use alphabets which are structured in some sense. We…
State reduction of finite automata plays a significant role in improving efficiency in formal verification, pattern recognition, and machine learning, where automata-based models are widely used. While deterministic automata have…
In this paper we introduce a new type of approximate state reductions where the behaviors of the reduced and the original automaton do not have to be identical, but they must match on all words of length less than or equal to some given…
A word w is called synchronizing (recurrent, reset, directed) word of a deterministic finite automaton (DFA) if w sends all states of the automaton on a unique state. Jan Cerny had found in 1964 a sequence of n-state complete DFA with…
This paper studies the algorithms for the minimisation of weighted automata. It starts with the definition of morphisms-which generalises and unifies the notion of bisimulation to the whole class of weighted automata-and the unicity of a…
Language models (LMs) are often expected to generate strings in some formal language; for example, structured data, API calls, or code snippets. Although LMs can be tuned to improve their adherence to formal syntax, this does not guarantee…
Finite-state automata are a very effective tool in natural language processing. However, in a variety of applications and especially in speech precessing, it is necessary to consider more general machines in which arcs are assigned weights…
The $n$th term of an automatic sequence is the output of a deterministic finite automaton fed with the representation of $n$ in a suitable numeration system. In this paper, instead of considering automatic sequences built on a numeration…
Consensus maximization is widely used for robust fitting in computer vision. However, solving it exactly, i.e., finding the globally optimal solution, is intractable. A* tree search, which has been shown to be fixed-parameter tractable, is…
The question if a deterministic finite automaton admits a software reset in the form of a so-called synchronizing word can be answered in polynomial time. In this paper, we extend this algorithmic question to deterministic automata beyond…
CCS can be considered as a most natural extension of finite state automata in which interaction is made possible thanks to parallel composition. We propose here a similar extension for top-down tree automata. We introduce a parallel…
We present a method for approximating context-free languages with one-counter automata. This approximation allows the reconstruction of parse trees of the original grammar. We identify a decidable superset of regular languages whose…
We consider the representational state complexity of unranked tree automata. The bottom-up computation of an unranked tree automaton may be either deterministic or nondeterministic, and further variants arise depending on whether the…
We follow language theoretic approach to synchronizing automata and \v{C}ern\'{y}'s conjecture initiated in a series of recent papers. We find a precise lower bound for the reset complexity of a principal ideal languages. Also we show a…
We introduce essential subtrees for terms (trees) and tree automata . There are some results concerning independent sets of subtrees and separable sets for a tree and an automaton.
We consider the complexity of equivalence and learning for multiplicity tree automata, i.e., weighted tree automata over a field. We first show that the equivalence problem is logspace equivalent to polynomial identity testing, the…