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The maximal existential (respectively, universal) width of an alternating finite automaton (AFA) on a string w is the maximal number of existential choices encountered in one branch (respectively, the maximal number of universal parallel branches)...

• We consider alternating finite automata (AFA) making a limited number of existential or universal choices in a computation.
• We provide upper and lower bounds for converting an AFA with limited universal width to a nondeterministic ...

For the given non-unary input alphabet Σ, a maximal prefix code h mapping strings over Σ to binary strings, and an optimal deterministic finite automaton (DFA) A with n states recognizing a language L over Σ, we consider the problem of how many ...

For a finite permutation group on n elements we show the following (and variants thereof) equivalences: (1) the permutation group is primitive, (2) in the transformation monoid generated by the group and any rank n − 1 mapping there exists, for ...

An automaton is synchronizing if there exists a word driving it into a definite state regardless of the starting state. For an n-state automaton the set of synchronizing words is a regular language that can be accepted by an automaton having 2 n −...

We continue the research on usefulness of information examining the effect of supplementary information on the complexity of solving a problem. We use DFAs for a formal setting. Given a problem (a regular language) L p r o b we measure the ...

Graph-walking automata analyze an input graph by moving between its nodes, following the edges. This paper investigates the effect of node-replacement graph homomorphisms and inverse homomorphisms on recognizability by these automata. For ...

Two strings are Simon's ∼ k-congruent if they have the same set of subsequences of length at most k. We study Simon's congruence closure of a string, which is regular by definition. Given a string w over an alphabet Σ, we present two ...

Population protocols are a model of computation in which an arbitrary number of indistinguishable finite-state agents interact in pairs. The goal of the agents is to decide by stable consensus whether their initial global configuration satisfies a ...$$$\mathcal{}$$\mathcal{}$$$$\mathrm{}$

Operations on regular languages that commute with any inverse alphabetic morphism are called 1-uniform transformations. In a previous work we have shown that these operations are encoded by operations on automata, called modifiers, ...

Two strings are Simon’s ${\sim }_k$-congruent if they have the same set of subsequences of length at most k. We study the Simon’s congruence closure of a string, which is regular by definition. Given a string w over an alphabet $\Sigma$, we present an efficient ...${}_{}$$$${}_{}$

We show that for any unambiguous finite automaton with n states there exists an unambiguous finite automaton with n + 1 ⋅ 2 n / 2 states that recognizes the complement language. This builds and improves upon a similar result by Jirásek ...

• We give a bound on the state complexity of complementing unambiguous automata.
• ...

We compare the succinctness of two monitoring systems for properties of infinite traces, namely parallel and regular monitors. Although a parallel monitor can be turned into an equivalent regular monitor, the cost of this transformation is a ...

The paper investigates the state complexity of two operations on regular languages, known as GF(2)-concatenation and GF(2)-inverse (Bakinova et al., “Formal languages over GF(2)”, LATA 2018), in the case of a one-symbol alphabet. The ...

We introduce the deterministic computational model of an iterated uniform finite-state transducer (iufst). An iufst performs the same length-preserving transduction on several left-to-right sweeps. The first sweep acts on the input ...

Tree width (respectively, string path width) measures the number of partial (respectively, complete) computations of a nondeterministic finite automaton (NFA) on a given input. We characterize polynomial and exponential growth rates of ...

Variants of the union and concatenation operations on formal languages are investigated, in which Boolean logic in the definitions (that is, conjunction and disjunction) is replaced with the operations in the two-element field GF(2) (...

Let NFA_b(q) denote the set of languages accepted by nondeterministic finite automata with q states over an alphabet with b letters. Let B_n denote the set of words of length n. We give a quadratic lower bound on the VC dimension of ...

We investigate the state complexity of the upward and downward closure and interior operations on commutative regular languages. Then, we systematically study the state complexity of these operations and of the shuffle operation on commutative ...

We introduce a subclass of the commutative regular languages that is characterized by the property that the state set of the minimal deterministic automaton can be written as a certain Cartesian product. This class behaves much better with respect ...${\mathrm{}}^{}$${}^{}$

It is shown that a two-way deterministic finite automaton (2DFA) with n states over an alphabet $\Sigma$ can be transformed to an equivalent one-way automaton (1DFA) with $|\Sigma |·\mathcal{F}(n)+1$ states, where $\mathcal{F}(n)={max}_{k=0}^n{k}^{n-k+1}\le {(n+1)}^{n+1}/{(ln(n+1)·e^{1-o(1)})}^{n+1}$.

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