Hasil untuk "cs.FL"

Jeffrey Shallit

We show that there is no automaton accepting the Tribonacci representations of $n$ and $x$ in parallel, where $ψ= 1.839\cdots$ is the Tribonacci constant, and $x= \lfloor n ψ\rfloor$. Similarly, there is no Tribonacci automaton generating the Sturmian characteristic word with slope $ψ-1$.

Sebastian Maneth, Martin Vu

We prove that for a given partial functional attributed tree transducer with monadic output, it is decidable whether or not an equivalent top-down transducer (with or without look-ahead) exists. We present a procedure that constructs an equivalent top-down transducer (with or without look-ahead) if it exists.

Jan Martens

In this paper, we present a proof of the NP-completeness of computing the smallest Deterministic Finite Automaton (DFA) that distinguishes two given regular languages as DFAs. A distinguishing DFA is an automaton that recognizes a language which is a subset of exactly one of the given languages. We establish the NP-hardness of this decision problem by providing a reduction from the Boolean Satisfiability Problem (SAT) to deciding the existence of a distinguishing automaton of a specific size.

Mikhail Volkov

We exhibit new conditions under which a primitive automaton is synchronizing. In particular, we show that the primitivity of an automaton forces its synchronizability whenever the automaton has either a letter of defect 1 or a word of rank 2.

Sebastian Maneth, Helmut Seidl, Martin Vu

We prove that functionality of compositions of top-down tree transducers is decidable by reducing the problem to the functionality of one top-down tree transducer with look-ahead.

Jeffrey Shallit

Let ftm = 0111010010001... be the analogue of the Thue-Morse sequence in Fibonacci representation. In this note we show how, using the Walnut theorem-prover, to obtain a measure of its complexity, previously studied by Jamet, Popoli, and Stoll. We strengthen one of their theorems and disprove one of their conjectures.

Thomas Kahl

It is shown that a higher-dimensional automaton is hhp-bisimilar to the free symmetric HDA generated by it. Consequently, up to hereditary history-preserving bisimilarity, ordinary HDAs and symmetric HDAs are models of concurrency with the same expressive power.

Joost Engelfriet

A binary relation on graphs is recursively enumerable if and only if it can be computed by a formula in monadic second-order logic. The latter means that the formula defines a set of graphs, in the usual way, such that each "computation graph" in that set determines a pair consisting of an input graph and an output graph.

Thijmen J. P. Krebs

We present a short new proof of Cobham's theorem without using Kronecker's approximation theorem, making it suitable for generalization beyond automatic sequences.

Michiel de Bondt

This paper contains results which arose from the research which led to arXiv:1801.10436, but which did not fit in arXiv:1801.10436. So arXiv:1801.10436 contains the highlight results, but there are more results which are interesting enough to be shared.

Tomohiro I, Dominik Köppl

We show that the number of all maximal $α$-gapped repeats and palindromes of a word of length $n$ is at most $3(π^2/6 + 5/2) αn$ and $7 (π^2 / 6 + 1/2) αn - 5 n - 1$, respectively.

Dmitry Ananichev

We present a new series of examples of binary slowly synchronizing automata with sink state. The reset threshold of the $n$-state automaton in this series is $\frac{n^2}{4}+2n-9$. This improves on the previously known lower bound for the maximum reset threshold of binary synchronizing $n$-state automata with sink state.

João Daniel Moreira

We prove that the meet level $m$ of the Trotter-Weil, $\mathsf{V}_m$ is not local for all $m \geq 1$, as conjectured in a paper by Kufleitner and Lauser. In order to show this, we explicitly provide a language whose syntactic semigroup is in $L \mathsf{V}_m$ and not in $\mathsf{V}_m*\mathsf{D}$.

Dietrich Kuske, Olena Prianychnykova

We prove that a trace monoid embeds into the queue monoid if and only if it embeds into the direct product of two free monoids. We also give a decidable characterization of these trace monoids.

Marina Maslennikova

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 complexity for languages related to slowly synchronizing automata and study uniqueness question for automata yielding the minimum of reset complexity.

Štěpán Holub

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 infinitely many positions.

Manfred Kudlek

We investigate the (non)-existence of universal automata for some classes of automata, such as finite automata and pushdown automata, and in particular the influence of the representation and encoding function. An alternative approach, using transition systems, is presented too.

C. Robinson Tompkins

In an attempt to classify all of the overlap-free morphisms constructively using the Latin-square morphism, we came across an interesting counterexample, the Leech square-free morphism. We generalize the combinatorial properties of the Leech square-free morphism to gain insights on a larger class of both overlap-free morphisms and square-free morphisms.

Ralf Stiebe, Sherzod Turaev

A capacity bounded grammar is a grammar whose derivations are restricted by assigning a bound to the number of every nonterminal symbol in the sentential forms. In the paper the generative power and closure properties of capacity bounded grammars and their Petri net controlled counterparts are investigated.

Yuan Gao, Sheng Yu

In this paper, we introduce the new concept of state complexity approximation, which is a further development of state complexity estimation. We show that this new concept is useful in both of the following two cases: the exact state complexities are not known and the state complexities have been obtained but are in incomprehensible form.