Related papers: Enumerating Finitary Processes
In the classic problem of sequence prediction, a predictor receives a sequence of values from an emitter and tries to guess the next value before it appears. The predictor masters the emitter if there is a point after which all of the…
Traditionally, finite automata theory has been used as a framework for the representation of possibly infinite sets of strings. In this work, we introduce the notion of second-order finite automata, a formalism that combines finite automata…
We study finite-state transducers and their power for transforming infinite words. Infinite sequences of symbols are of paramount importance in a wide range of fields, from formal languages to pure mathematics and physics. While finite…
Every language recognized by a non-deterministic finite automaton can be recognized by a deterministic automaton, at the cost of a potential increase of the number of states, which in the worst case can go from $n$ states to $2^n$ states.…
Continuous-time stochastic processes pervade everyday experience, and the simulation of models of these processes is of great utility. Classical models of systems operating in continuous-time must typically track an unbounded amount of…
Recently, the problem of obtaining a short regular expression equivalent to a given finite automaton has been intensively investigated. Algorithms for converting finite automata to regular expressions have an exponential blow-up in the…
To identify potential universal cellular automata, a method is developed to measure information processing capacity of elementary cellular automata. We consider two features of cellular automata: Ability to store information, and ability to…
Determinisation and completion of finite tree automata are important operations with applications in program analysis and verification. However, the complexity of the classical procedures for determinisation and completion is high. They are…
Cellular automata are arrays of finite state machines that can exist in a finite number of states. These machines update their states simultaneously based on specific local rules that govern their interactions. This framework provides a…
We prove that endowing a real-time probabilistic or quantum computer with the ability of postselection increases its computational power. For this purpose, we provide a new model of finite automata with postselection, and compare it with…
Simulating the stochastic evolution of real quantities on a digital computer requires a trade-off between the precision to which these quantities are approximated, and the memory required to store them. The statistical accuracy of the…
Quantum computing is a new model of computation, based on quantum physics. Quantum computers can be exponentially faster than conventional computers for problems such as factoring. Besides full-scale quantum computers, more restricted…
Model checking properties are often described by means of finite automata. Any particular such automaton divides the set of infinite trees into finitely many classes, according to which state has an infinite run. Building the full type…
The simulation of deterministic pushdown automata defined over a one-letter alphabet by finite state automata is investigated from a descriptional complexity point of view. We show that each unary deterministic pushdown automaton of size s…
We introduce and investigate forgetting 1-limited automata, which are single-tape Turing machines that, when visiting a cell for the first time, replace the input symbol in it by a fixed symbol, so forgetting the original contents. These…
A finitary automaton group is a group generated by an invertible, deterministic finite-state letter-to-letter transducer whose only cycles are self-loops at an identity state. We show that, for this presentation of finite groups, the…
Inspired by distributed algorithms, we introduce a new class of finite graph automata that recognize precisely the graph languages definable in monadic second-order logic. For the cases of words and trees, it has been long known that the…
Stochastic languages are the languages recognized by probabilistic finite automata (PFAs) with cutpoint over the field of real numbers. More general computational models over the same field such as generalized finite automata (GFAs) and…
We investigate means of efficient computation of the simulation relation over symbolic finite automata (SFAs), i.e., finite automata with transitions labeled by predicates over alphabet symbols. In one approach, we build on the algorithm by…
This is Chapter 24 in the "AutoMathA" handbook. Finite automata have been used effectively in recent years to define infinite groups. The two main lines of research have as their most representative objects the class of automatic groups…