Related papers: Syntactic Complexity of Star-Free Languages
We consider some questions about formal languages that arise when inverses of letters, words and languages are defined. The reduced representation of a language over the free monoid is its unique equivalent representation in the free group.…
We revisit the phenomenon of syntactic complexity convergence in conversational interaction, originally found for English dialogue, which has theoretical implication for dialogical concepts such as mutual understanding. We use a modified…
String complexity is defined as the cardinality of a set of all distinct words (factors) of a given string. For two strings, we introduce the joint string complexity as the cardinality of a set of words that are common to both strings.…
A turn in a computation of a pushdown automaton is a switch from a phase in which the height of the pushdown store increases to a phase in which it decreases. Given a pushdown or one-counter automaton, we consider, for each string in its…
In a previous article, we have introduced the problem of local generation of languages, where the communication underlying the generation procedure is captured by a simplicial complex. We study in details this problem for the language of…
The set of synchronizing words of a given $n$-state automaton forms a regular language recognizable by an automaton with $2^n - n$ states. The size of a recognizing automaton for the set of synchronizing words is linked to computational…
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…
The present paper presents and proves a proposition concerning the time complexity of finite languages. It is shown herein, that for any finite language (a language for which the set of words composing it is finite) there is a Turing…
This work is a study of the expressive power of unambiguity in the case of automata over infinite trees. An automaton is called unambiguous if it has at most one accepting run on every input, the language of such an automaton is called an…
While state-of-the-art neural network models continue to achieve lower perplexity scores on language modeling benchmarks, it remains unknown whether optimizing for broad-coverage predictive performance leads to human-like syntactic…
This paper deals with descriptive complexity of picture languages of any dimension by syntactical fragments of existential second-order logic. - We uniformly generalize to any dimension the characterization by Giammarresi et al.…
Hyperproperties lift conventional trace-based languages from a set of execution traces to a set of sets of executions. From a formal-language perspective, these are sets of sets of words, namely hyperlanguages. Hyperautomata are based on…
A generalization of numeration system in which the set N of the natural numbers is recognizable by finite automata can be obtained by describing a lexicographically ordered infinite regular language. Here we show that if P belonging to Q[x]…
We show that for any monoid M, the family of languages accepted by M-automata (or equivalently, generated by regular valence grammars over M) is completely determined by that part of M which lies outside the maximal ideal. Hence, every such…
We study the satisfiability problem of symbolic finite automata and decompose it into the satisfiability problem of the theory of the input characters and the monadic second-order theory of the indices of accepted words. We use our…
Nowadays the question `what is complexity?' is a challenge to be answered. This question is triggering a great quantity of works in the frontier of physics, biology, mathematics and computer science. Even more when this century has been…
We construct a hierarchy of regular languages such that the current language in the hierarchy can be accepted by 1-way quantum finite automata with a probability smaller than the corresponding probability for the preceding language in the…
As speakers turn their thoughts into sentences, they maintain a balance between the complexity of words and syntax. However, it is unclear whether this syntax-lexicon tradeoff is unique to the spoken language production that is under the…
SYNTAGMA is a rule-based parsing system, structured on two levels: a general parsing engine and a language specific grammar. The parsing engine is a language independent program, while grammar and language specific rules and resources are…
In this paper, we study the word problem for automaton semigroups and automaton groups from a complexity point of view. As an intermediate concept between automaton semigroups and automaton groups, we introduce automaton-inverse semigroups,…