Related papers: Maximal State Complexity and Generalized de Bruijn…
In this work we construct an automaton for the commutative closure of a given regular group language. The number of states of the resulting automaton is bounded by the number of states of the original automaton, raised to the power of the…
We generalise a multiple string pattern matching algorithm, recently proposed by Fredriksson and Grabowski [J. Discr. Alg. 7, 2009], to deal with arbitrary dictionaries on an alphabet of size $s$. If $r_m$ is the number of words of length…
We study the state complexity of binary operations on regular languages over different alphabets. It is known that if $L'_m$ and $L_n$ are languages of state complexities $m$ and $n$, respectively, and restricted to the same alphabet, the…
If an infinite non-periodic word is uniformly recurrent or is of bounded repetition, then the limit of its periodicity complexity is infinity. Moreover, there are uniformly recurrent words with the periodicity complexity arbitrarily high at…
Given a subset of states $S$ of a deterministic finite automaton and a word $w$, the preimage is the subset of all states mapped to a state in $S$ by the action of $w$. We study three natural problems concerning words giving certain…
We present a new characteristic of a regular ideal language called reset complexity. We find some bounds on the reset complexity in terms of the state complexity of a given language. We also compare the reset complexity and the state…
The height of a piecewise-testable language $L$ is the maximum length of the words needed to define $L$ by excluding and requiring given subwords. The height of $L$ is an important descriptive complexity measure that has not yet been…
We show that the Word Problem in finitely generated subgroups of $\textsf{GL}_d(\mathbb{Z})$ can be solved in linear average-case complexity. This is done under the bit-complexity model, which accounts for the fact that large integers are…
We prove that the word problem in the mapping class group of the once-punctured surface of genus g has complexity O(|w|^2 g for |w| > log(g) where |w| is the length of the word in a (standard) set of generators. The corresponding bound in…
We provide an exact estimate on the maximal subword complexity for quasiperiodic infinite words. To this end we give a representation of the set of finite and of infinite words having a certain quasiperiod q via a finite language derived…
A right ideal is a language L over an alphabet A that satisfies L = LA*. We show that there exists a stream (sequence) (R_n : n \ge 3) of regular right ideal languages, where R_n has n left quotients and is most complex under the following…
In this article we undertake a study of extension complexity from the perspective of formal languages. We define a natural way to associate a family of polytopes with binary languages. This allows us to define the notion of extension…
I study the state complexity of binary operations on regular languages over different alphabets. It is well known that if $L'_m$ and $L_n$ are languages restricted to be over the same alphabet, with $m$ and $n$ quotients, respectively, the…
We introduced the notation of a set of prohibitions and give definitions of a complete set and a crucial word with respect to a given set of prohibitions. We consider 3 particular sets which appear in different areas of mathematics and for…
In this paper, we assess the complexity results of formalisms that describe the feature theories used in computational linguistics. We show that from these complexity results no immediate conclusions can be drawn about the complexity of the…
In this note we provide a (decidable) graph-structural characterisation of the infiniteness of $L(w_1, ..., w_k)$, where $L(w_1, ..., w_k) = \{w \in A^* | |w|_{w_1} = \cdots = |w|_{w_k}\}$ is the set of all words that contain the same…
A language $L$ over an alphabet $\Sigma$ is prefix-convex if, for any words $x,y,z\in\Sigma^*$, whenever $x$ and $xyz$ are in $L$, then so is $xy$. Prefix-convex languages include right-ideal, prefix-closed, and prefix-free languages. We…
The degree of a CSP instance is the maximum number of times that any variable appears in the scopes of constraints. We consider the approximate counting problem for Boolean CSP with bounded-degree instances, for constraint languages…
We investigate the nondeterministic state complexity of basic operations for suffix-free regular languages. The nondeterministic state complexity of an operation is the number of states that are necessary and sufficient in the worst-case…
Let $A_q$ be a $q$-letter alphabet and $w$ be a right infinite word on this alphabet. A subword of $w$ is a block of consecutive letters of $w$. The subword complexity function of $w$ assigns to each positive integer $n$ the number $f_w(n)$…