Related papers: Nondeterministic Syntactic Complexity
Finite-state morphology in the general tradition of the Two-Level and Xerox implementations has proved very successful in the production of robust morphological analyzer-generators, including many large-scale commercial systems. However, it…
We propose a formalism for representation of finite languages, referred to as the class of IDL-expressions, which combines concepts that were only considered in isolation in existing formalisms. The suggested applications are in natural…
We study density of rational languages under shift invariant probability measures on spaces of two-sided infinite words, which generalizes the classical notion of density studied in formal languages and automata theory. The density for a…
In dynamical systems such as cellular automata and iterated maps, it is often useful to look at a language or set of symbol sequences produced by the system. There are well-established classification schemes, such as the Chomsky hierarchy,…
Semiautomata form a rich class of sequence-processing algorithms with applications in natural language processing, robotics, computational biology, and data mining. We establish the first Statistical Query hardness result for semiautomata…
Mechanistic interpretability aims to explain neural model behaviour by reverse-engineering learned computational structure into human-understandable components. Without a formal framework, however, mechanistic explanations cannot be…
We characterize complete deterministic finite automata with two input letters in which every non-empty set of states occurs as the image of the whole state set under the action of a suitable input word. The characterization leads to a…
In this paper we characterize the definiteness of the discrete symplectic system, study a nonhomogeneous discrete symplectic system, and introduce the minimal and maximal linear relations associated with these systems. Fundamental…
The essential step of abstraction-based control synthesis for nonlinear systems to satisfy a given specification is to obtain a finite-state abstraction of the original systems. The complexity of the abstraction is usually the dominating…
The equivalence of finite automata and regular expressions dates back to the seminal paper of Kleene on events in nerve nets and finite automata from 1956. In the present paper we tour a fragment of the literature and summarize results on…
Controller synthesis techniques for continuous systems with respect to temporal logic specifications typically use a finite-state symbolic abstraction of the system. Constructing this abstraction for the entire system is computationally…
The regular autonomous asynchronous systems are the non-deterministic Boolean dynamical systems and universality means the greatest in the sense of the inclusion. The paper gives four definitions of symmetry of these systems in a slightly…
We show that every regular language defines a unique nondeterministic finite automaton (NFA), which we call "\'atomaton", whose states are the "atoms" of the language, that is, non-empty intersections of complemented or uncomplemented left…
Modal automata are a classic formal model for component-based systems that comes equipped with a rich specification theory supporting abstraction, refinement and compositional reasoning. In recent years, quantitative variants of modal…
Graphical models in probability and statistics are a core concept in the area of probabilistic reasoning and probabilistic programming-graphical models include Bayesian networks and factor graphs. In this paper we develop a new model of…
First-order linear temporal logic (FOLTL) is a flexible and expressive formalism capable of naturally describing complex behaviors and properties. Although the logic is in general highly undecidable, the idea of using it as a specification…
The state complexity of basic operations on finite languages (considering complete DFAs) has been in studied the literature. In this paper we study the incomplete (deterministic) state and transition complexity on finite languages of…
We study expression learning problems with syntactic restrictions and introduce the class of finite-aspect checkable languages to characterize symbolic languages that admit decidable learning. The semantics of such languages can be defined…
The ambiguity of a nondeterministic finite automaton (NFA) N for input size n is the maximal number of accepting computations of N for an input of size n. For all k, r 2 N we construct languages Lr,k which can be recognized by NFA's with…
This paper proposes new semantics for nondeterministic program execution, replacing the standard relational semantics for propositional dynamic logic (PDL). Under these new semantics, program execution is represented as fundamentally…