Related papers: Maximal automatic complexity and context-free lang…
Generalizing the notion of automatic complexity of individual strings due to Shallit and Wang, we define the automatic complexity $A(E)$ of an equivalence relation $E$ on a finite set $S$ of strings. We prove that the problem of determining…
The automatic complexity of a finite word (string) is an analogue for finite automata of Sipser's distinguishing complexity (1983) and was introduced by Shallit and Wang (2001). For a finite alphabet $\Sigma$ of at least two elements, we…
We answer two open questions by (Gruber, Holzer, Kutrib, 2009) on the state-complexity of representing sub- or superword closures of context-free grammars (CFGs): (1) We prove a (tight) upper bound of $2^{\mathcal{O}(n)}$ on the size of…
We discuss the computational complexity of context-free languages, concentrating on two well-known structural properties---immunity and pseudorandomness. An infinite language is REG-immune (resp., CFL-immune) if it contains no infinite…
Given a finite alphabet $\Sigma$ and a right-infinite word $\bf w$ over $\Sigma$, we define the Lie complexity function $L_{\bf w}:\mathbb{N}\to \mathbb{N}$, whose value at $n$ is the number of conjugacy classes (under cyclic shift) of…
We introduce $L^2_{K,P}$, a monadic second-order language for reasoning about trees which characterizes the strongly Context-Free Languages in the sense that a set of finite trees is definable in $L^2_{K,P}$ iff it is (modulo a projection)…
Let $A^*$ denote the free monoid generated by a finite nonempty set $A.$ In this paper we introduce a new measure of complexity of languages $L\subseteq A^*$ defined in terms of the semigroup structure on $A^*.$ For each $L\subseteq A^*,$…
Let $x$ be an $m$-sequence, a maximal length sequence produced by a linear feedback shift register. We show that $x$ has maximal subword complexity function in the sense of Allouche and Shallit. We show that this implies that the…
We present new descriptive complexity characterisations of classes REG (regular languages), LCFL (linear context-free languages) and CFL (context-free languages) as restrictions on inference rules, size of formulae and permitted connectives…
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…
We study various complexity properties of suffix-free regular languages. The quotient complexity of a regular language $L$ is the number of left quotients of $L$; this is the same as the state complexity of $L$. A regular language $L'$ is a…
For a complexity function $C$, the lower and upper $C$-complexity rates of an infinite word $\mathbf{x}$ are \[ \underline{C}(\mathbf x)=\liminf_{n\to\infty} \frac{C(\mathbf{x}\upharpoonright n)}n,\quad \overline{C}(\mathbf…
This paper concerns $\mu$-limit sets of cellular automata: sets of configurations made of words whose probability to appear does not vanish with time, starting from an initial $\mu$-random configuration. More precisely, we investigate the…
Nonterminal complexity of a context-free language is the smallest possible number of nonterminals in its generating grammar. While in general case nonterminal complexity computation problem is unsolvable, it can be computed for different…
We present a new proof that $O_2$ is a multiple context-free language. It contrasts with a recent proof by Salvati (2015) in its avoidance of concepts that seem specific to two-dimensional geometry, such as the complex exponential function.…
We relate two measures of complexity of regular languages. The first is syntactic complexity, that is, the cardinality of the syntactic semigroup of the language. That semigroup is isomorphic to the semigroup of transformations of states…
The complexity class LOGCFL (resp., LOGDCFL) consists of all languages that are many-one reducible to context-free (resp., deterministic context-free) languages using logarithmic space. These complexity classes have been studied over five…
The atoms of a regular language are non-empty intersections of complemented and uncomplemented quotients of the language. Tight upper bounds on the number of atoms of a language and on the quotient complexities of atoms are known. We…
The subword complexity of a finite word $w$ of length $N$ is a function which associates to each $n\le N$ the number of all distinct subwords of $w$ having the length $n$. We define the \emph{maximal complexity} C(w) as the maximum of the…
We study the membership problem to context-free languages L (CFLs) on probabilistic words, that specify for each position a probability distribution on the letters (assuming independence across positions). Our task is to compute, given a…