Related papers: The word problem distinguishes counter languages

Let $\mathcal{P}(\Sigma^*)$ be the semiring of languages, and consider its subset $\mathcal{P}(\Sigma)$. In this paper we define the language recognized by a weighted automaton over $\mathcal{P}(\Sigma)$ and a one-letter alphabet.…

We look into the problems of comparing nondeterministic discounted-sum automata on finite and infinite words. That is, the problems of checking for automata $A$ and $B$ whether or not it holds that for all words $w$, $A(w)=B(w), A(w) \leq…

Probabilistic automata are an extension of nondeterministic finite automata in which transitions are annotated with probabilities. Despite its simplicity, this model is very expressive and many of the associated algorithmic questions are…

We prove that some fairly basic questions on automata reading infinite words depend on the models of the axiomatic system ZFC. It is known that there are only three possibilities for the cardinality of the complement of an omega-language…

Some of the most interesting and important results concerning quantum finite automata are those showing that they can recognize certain languages with (much) less resources than corresponding classical finite automata…

Several insertion operations are studied applied to languages accepted by one-way and two-way deterministic reversal-bounded multicounter machines. These operations are defined by the ideals obtained from relations such as the prefix,…

We consider the state complexity of basic operations on tree languages recognized by deterministic unranked tree automata. For the operations of union and intersection the upper and lower bounds of both weakly and strongly deterministic…

We prove that language equivalence of deterministic one-counter automata is NL-complete. This improves the superpolynomial time complexity upper bound shown by Valiant and Paterson in 1975. Our main contribution is to prove that two…

Data automata on data words is a decidable model proposed by Boja\'nczyk et al. in 2006. Class automata, introduced recently by Boja\'nczyk and Lasota, is an extension of data automata which unifies different automata models on data words.…

This paper studies the complexity of operations on finite automata and the complexity of their decision problems when the alphabet is unary. Let $n$ denote the maximum of the number of states of the input finite automata considered in the…

The downward closure of a language is the set of all (not necessarily contiguous) subwords of its members. It is well-known that the downward closure of every language is regular. Moreover, recent results show that downward closures are…

In this work we use a framework of finite-state automata constructions based on equivalences over words to provide new insights on the relation between well-known methods for computing the minimal deterministic automaton of a language.

We prove that a group has word problem that is a growing context-sensitive language precisely if its word problem can be solved using a non-deterministic Cannon's algorithm (the deterministic algorithms being defined by Goodman and…

The problem of inclusion of the language accepted by timed automaton $A$ (e.g., the implementation) in the language accepted by $B$ (e.g., the specification) is, in general, undecidable in the class of non-deterministic timed automata. In…

The deterministic membership problem for timed automata asks whether the timed language recognised by a nondeterministic timed automaton can be recognised by a deterministic timed automaton. We show that the problem is decidable when the…

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 projected language of a general deterministic automaton with $n$ states is recognizable by a deterministic automaton with $2^{n-1} + 2^{n-m} - 1$ states, where $m$ denotes the number of states incident to unobservable non-loop…

Automata over infinite objects are a well-established model with applications in logic and formal verification. Traditionally, acceptance in such automata is defined based on the set of states visited infinitely often during a run. However,…

In this paper we consider the class of lambda-nondeterministic linear automata as a model of the class of linear languages. As usual in other automata models, lambda-moves do not increase the acceptance power. The main contribution of this…

Formal languages over infinite alphabets serve as abstractions of structures and processes carrying data. Automata models over infinite alphabets, such as classical register automata or, equivalently, nominal orbit-finite automata, tend to…