Related papers: Fine-Grained Complexity of Ambiguity Problems on A…
In many data classification problems, there is no linear relationship between an explanatory and the dependent variables. Instead, there may be ranges of the input variable for which the observed outcome is signficantly more or less likely.…
Complementation and determinization are two fundamental notions in automata theory. The close relationship between the two has been well observed in the literature. In the case of nondeterministic finite automata on finite words (NFA),…
Deterministic 2-head finite automata which are machines that process an input word from both ends are analyzed for their ability to perform reversible computations. This implies that the automata are backward deterministic, enabling unique…
We conceive finite automata as dynamical systems on discontinuum and investigate their factors. Factors of finite automata include many well-known simple dynamical systems, e.g. hyperbolic systems and systems with finite attractors. In the…
Unambiguous non-deterministic finite automata have intermediate expressive power and succinctness between deterministic and non-deterministic automata. It has been conjectured that every unambiguous non-deterministic one-way finite…
We introduce a logic to express structural properties of automata with string inputs and, possibly, outputs in some monoid. In this logic, the set of predicates talking about the output values is parametric, and we provide sufficient…
We introduce Symbolic Alternating Finite Automata (s-AFA) as an expressive, succinct, and decidable model for describing sets of finite sequences over arbitrary alphabets. Boolean operations over s-AFAs have linear complexity, which is in…
We explore bounds of {\em time-space tradeoffs} in language recognition on {\em two-way finite automata} for some special languages. We prove: (1) a time-space tradeoff upper bound for recognition of the languages $L_{EQ}(n)$ on {\em…
This paper connects the classes of weighted alternating finite automata (WAFA), weighted finite tree automata (WFTA), and polynomial automata (PA). First, we investigate the use of trees in the run semantics for weighted alternating…
Let $G$ be a directed graph on $n$ vertices. Given an integer $k<=n$, the SIMPLE $k$-PATH problem asks whether there exists a simple $k$-path in $G$. In case $G$ is weighted, the MIN-WT SIMPLE $k$-PATH problem asks for a simple $k$-path in…
It is an open problem to characterize the class of languages recognized by quantum finite automata (QFA). We examine some necessary and some sufficient conditions for a (regular) language to be recognizable by a QFA. For a subclass of…
The complexity and decidability of various decision problems involving the shuffle operation are studied. The following three problems are all shown to be $NP$-complete: given a nondeterministic finite automaton (NFA) $M$, and two words $u$…
In automata theory, while determinisation provides a standard route to solving many common problems in automata theory, some weak forms of nondeterminism can be dealt with in some problems without costly determinisation. For example, the…
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 introduce a new complexity measure for finite strings using probabilistic finite-state automata (PFAs), in the same spirit as existing notions employing DFAs and NFAs, and explore its properties. The PFA complexity $A_P(x)$ is the least…
We show that there are quantum devices that accept all regular languages and that are exponentially more concise than deterministic finite automata (DFA). For this purpose, we introduce a new computing model of {\it one-way quantum finite…
We show that a special case of the Feferman-Vaught composition theorem gives rise to a natural notion of automata for finite words over an infinite alphabet, with good closure and decidability properties, as well as several logical…
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 consider two-variable first-order logic $\text{FO}^2$ and its quantifier alternation hierarchies over both finite and infinite words. Our main results are forbidden patterns for deterministic automata (finite words) and for Carton-Michel…
A discounted-sum automaton (NDA) is a nondeterministic finite automaton with edge weights, valuing a run by the discounted sum of visited edge weights. More precisely, the weight in the i-th position of the run is divided by $\lambda^i$,…