Related papers: The complexity of downward closure comparisons
The question if a deterministic finite automaton admits a software reset in the form of a so-called synchronizing word can be answered in polynomial time. In this paper, we extend this algorithmic question to deterministic automata beyond…
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…
For a non-negative integer $k$, a language is $k$-piecewise test\-able ($k$-PT) if it is a finite boolean combination of languages of the form $\Sigma^* a_1 \Sigma^* \cdots \Sigma^* a_n \Sigma^*$ for $a_i\in\Sigma$ and $0\le n \le k$. We…
A notion of alternating timed automata is proposed. It is shown that such automata with only one clock have decidable emptiness problem over finite words. This gives a new class of timed languages which is closed under boolean operations…
The problem of \emph{regular separability} asks, given two languages $K$ and $L$, whether there exists a regular language $S$ with $K\subseteq S$ and $S\cap L=\emptyset$. This problem has recently been studied for various classes of…
We consider questions related to the structure of infinite words (over an integer alphabet) with bounded additive complexity, i.e., words with the property that the number of distinct sums exhibited by factors of the same length is bounded…
We exhibit the construction of a deterministic automaton that, given k > 0, recognizes the (regular) language of k-differentiable words. Our approach follows a scheme of Crochemore et al. based on minimal forbidden words. We extend this…
A language is dense if the set of all infixes (or subwords) of the language is the set of all words. Here, it is shown that it is decidable whether the language accepted by a nondeterministic Turing machine with a one-way read-only input…
Counter automata are more powerful versions of finite-state automata where addition and subtraction operations are permitted on a set of n integer registers, called counters. We show that the word problem of $\Z^n$ is accepted by a…
In a one-counter automaton (OCA), one can produce a letter from some finite alphabet, increment and decrement the counter by one, or compare it with constants up to some threshold. It is well-known that universality and language inclusion…
A separator for two languages is a third language containing the first one and disjoint from the second one. We investigate the following decision problem: given two regular input languages, decide whether there exists a locally testable…
Given a language L and a nondeterministic finite automaton M, we consider whether we can determine efficiently (in the size of M) if M accepts at least one word in L, or infinitely many words. Given that M accepts at least one word in L, we…
Checking whether two pushdown automata with restricted silent actions are weakly bisimilar was shown decidable by S\'enizergues (1998, 2005). We provide the first known complexity upper bound for this famous problem, in the equivalent…
A class of languages C is perfect if it is closed under Boolean operations and the emptiness problem is decidable. Perfect language classes are the basis for the automata-theoretic approach to model checking: a system is correct if the…
For substructural logics with contraction or weakening admitting cut-free sequent calculi, proof search was analyzed using well-quasi-orders on $\mathbb{N}^d$ (Dickson's lemma), yielding Ackermannian upper bounds via controlled bad-sequence…
We introduce the constrained topological sorting problem (CTS): given a regular language K and a directed acyclic graph G with labeled vertices, determine if G has a topological sort that forms a word in K. This natural problem applies to…
The store language of a machine of some arbitrary type is the set of all store configurations (state plus store contents but not the input) that can appear in an accepting computation. New algorithms and characterizations of store languages…
We study the state complexity of regular operations in the class of ideal languages. A language L over an alphabet Sigma is a right (left) ideal if it satisfies L = L Sigma* (L = Sigma* L). It is a two-sided ideal if L = Sigma* L Sigma *,…
The regular separability problem asks, for two given languages, if there exists a regular language including one of them but disjoint from the other. Our main result is decidability, and PSpace-completeness, of the regular separability…
The complexity class DP is the class of all languages that are the intersection of a language in NP and a language in coNP. It was conjectured that recognizing a facet for the knapsack polytope is DP-complete. We provide a positive answer…