Related papers: On the Complexity of Intersection Non-emptiness fo…
The class of local languages is a well-known subclass of the regular languages that admits many equivalent characterizations. In this short note we establish the PSPACE-completeness of the problem of determining, given as input a…
We study the satisfiability problem of symbolic finite automata and decompose it into the satisfiability problem of the theory of the input characters and the monadic second-order theory of the indices of accepted words. We use our…
We study the emptiness and $\lambda$-reachability problems for unary and binary Probabilistic Finite Automata (PFA) and characterise the complexity of these problems in terms of the degree of ambiguity of the automaton and the size of its…
Families of deterministic finite automata (FDFA) represent regular $\omega$-languages through their ultimately periodic words (UP-words). An FDFA accepts pairs of words, where the first component corresponds to a prefix of the UP-word, and…
We investigate the intersection problem for finite semigroups, which asks for a given set of regular languages, represented by recognizing morphisms to finite semigroups, whether there exists a word contained in their intersection. We…
For general input automata, there exist regular constraint languages such that asking if a given input automaton admits a synchronizing word in the constraint language is PSPACE-complete or NP-complete. Here, we investigate this problem for…
A complete deterministic finite (semi)automaton (DFA) with a set of states $Q$ is \emph{completely reachable} if every nonempty subset of $Q$ is the image of the action of some word applied to $Q$. The concept of completely reachable…
Partially ordered automata are automata where the transition relation induces a partial order on states. The expressive power of partially ordered automata is closely related to the expressivity of fragments of first-order logic on finite…
In the present work, we lay out a new theory showing that all automata can always be co-lexicographically partially ordered, and an intrinsic measure of their complexity can be defined and effectively determined, namely, the minimum width…
We realize constant-space quantum computation by measure-many two-way quantum finite automata and evaluate their language recognition power by analyzing patterns of their exotic behaviors and by exploring their structural properties. In…
We pose the fine-grained hardness hypothesis that the textbook algorithm for the NFA Acceptance problem is optimal up to subpolynomial factors, even for dense NFAs and fixed alphabets. We show that this barrier appears in many variations…
An index for a finite automaton is a powerful data structure that supports locating paths labeled with a query pattern, thus solving pattern matching on the underlying regular language. In this paper, we solve the long-standing problem of…
We study the basic regular expression intersection testing problem, which asks to determine whether the intersection of the languages of two regular expressions is nonempty. A textbook solution to this problem is to construct the…
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 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…
Nondeterministic automata may be viewed as succinct programs implementing deterministic automata, i.e. complete specifications. Converting a given deterministic automaton into a small nondeterministic one is known to be computationally very…
In a simple pattern matching problem one has a pattern $w$ and a text $t$, which are words over a finite alphabet $\Sigma$. One may ask whether $w$ occurs in $t$, and if so, where? More generally, we may have a set $P$ of patterns and a set…
We present an efficient algorithm for checking language equivalence of states in top-down deterministic finite tree automata (DFTAs). Unlike string automata, tree automata operate over hierarchical structures, posing unique challenges for…
We investigate the decidability of the emptiness problem for three classes of distributed automata. These devices operate on finite directed graphs, acting as networks of identical finite-state machines that communicate in an infinite…
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…