Related papers: Most Complex Non-Returning Regular Languages
Let $A_N$ denote nondeterministic automatic complexity and \[ L_{k,c}=\{x\in [k]^* : A_N(x)> |x|/c\}. \] In particular, $L_{k,2}$ is the language of all $k$-ary words for which $A_N$ is maximal, while $L_{k,3}$ gives a rough dividing line…
We introduce a new measure on regular languages: their nondeterministic syntactic complexity. It is the least degree of any extension of the `canonical boolean representation' of the syntactic monoid. Equivalently, it is the least number of…
A language $L$ is the orthogonal catenation of languages $L_1$ and $L_2$ if every word of $L$ can be written in a unique way as a catenation of a word in $L_1$ and a word in $L_2$. We establish a tight bound for the state complexity of…
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 study the class of languages that have membership proofs which can be verified by real-time finite-state machines using only a constant number of random bits, regardless of the size of their inputs. Since any further restriction on the…
In this paper, we study the static cell probe complexity of non-adaptive data structures that maintain a subset of $n$ points from a universe consisting of $m=n^{1+\Omega(1)}$ points. A data structure is defined to be non-adaptive when the…
Regular expressions constitute a fundamental notion in formal language theory and are frequently used in computer science to define search patterns. A classic algorithm for these problems constructs and simulates a non-deterministic finite…
We give an upper bound of $n((n-1)!-(n-3)!)$ for the possible largest size of a subsemigroup of the full transformational semigroup over $n$ elements consisting only of nonpermutational transformations. As an application we gain the same…
Finite automata whose computations can be reversed, at any point, by knowing the last k symbols read from the input, for a fixed k, are considered. These devices and their accepted languages are called k-reversible automata and k-reversible…
We investigate certain word-construction games with variable turn orders. In these games, Alice and Bob take turns on choosing consecutive letters of a word of fixed length, with Alice winning if the result lies in a predetermined target…
We define a new class of languages of $\omega$-words, strictly extending $\omega$-regular languages. One way to present this new class is by a type of regular expressions. The new expressions are an extension of $\omega$-regular expressions…
Improving the previously known best bound, we show that any recursively enumerable language can be generated with a non-returning parallel communicating (PC) grammar system having six context-free components. We also present a non-returning…
We give a new characterization of $\mathsf{NL}$ as the class of languages whose members have certificates that can be verified with small error in polynomial time by finite state machines that use a constant number of random bits, as…
A regular language has the zero-one law if its asymptotic density converges to either zero or one. We prove that the class of all zero-one languages is closed under Boolean operations and quotients. Moreover, we prove that a regular…
We introduce a subclass of the commutative regular languages that is characterized by the property that the state set of the minimal deterministic automaton can be written as a certain Cartesian product. This class behaves much better with…
Recently, an infinite hierarchy of languages accepted by stateless deterministic pushdown automata has been established based on the number of pushdown symbols. However, the witness language for the n-th level of the hierarchy is over an…
This paper proposes an extension to classical regular expressions by the addition of two operators allowing the inclusion of boolean formulae from the zeroth order logic. These expressions are called constrained expressions. The associated…
We present a trichotomy theorem for the quantum query complexity of regular languages. Every regular language has quantum query complexity Theta(1), ~Theta(sqrt n), or Theta(n). The extreme uniformity of regular languages prevents them from…
We prove the non-existence of recurrent words with constant Abelian complexity containing 4 or more distinct letters. This answers a question of Richomme et al.
We consider the language of $\Delta_0$-formulas with list terms interpreted over hereditarily finite list superstructures. We study the complexity of reasoning in extensions of the language of $\Delta_0$-formulas with non-standard list…