299 research outputs found
Synchronizing automata with random inputs
We study the problem of synchronization of automata with random inputs. We
present a series of automata such that the expected number of steps until
synchronization is exponential in the number of states. At the same time, we
show that the expected number of letters to synchronize any pair of the famous
Cerny automata is at most cubic in the number of states
Finitely generated ideal languages and synchronizing automata
We study representations of ideal languages by means of strongly connected
synchronizing automata. For every finitely generated ideal language L we
construct such an automaton with at most 2^n states, where n is the maximal
length of words in L. Our constructions are based on the De Bruijn graph.Comment: Submitted to WORDS 201
The Complexity of Finding Reset Words in Finite Automata
We study several problems related to finding reset words in deterministic
finite automata. In particular, we establish that the problem of deciding
whether a shortest reset word has length k is complete for the complexity class
DP. This result answers a question posed by Volkov. For the search problems of
finding a shortest reset word and the length of a shortest reset word, we
establish membership in the complexity classes FP^NP and FP^NP[log],
respectively. Moreover, we show that both these problems are hard for
FP^NP[log]. Finally, we observe that computing a reset word of a given length
is FNP-complete.Comment: 16 pages, revised versio
Slowly synchronizing automata and digraphs
We present several infinite series of synchronizing automata for which the
minimum length of reset words is close to the square of the number of states.
These automata are closely related to primitive digraphs with large exponent.Comment: 13 pages, 5 figure
Giant thermoemf in multiterminal superconductor/normal metal mesoscopic structures
We considered a mesoscopic superconductor/normal metal (S/N) structure in
which the N reservoirs are maintained at different temperatures. It is shown
that in the absence of current between the N reservoirs a voltage difference
arises between the superconducting and normal conductors. The voltage
oscillates with increasing phase difference between the
superconductors, and its magnitude does not depend on the small parameter
Comment: Resubmited, some changes to Text and Figure
Complexity of checking whether two automata are synchronized by the same language
A deterministic finite automaton is said to be synchronizing if it has a
reset word, i.e. a word that brings all states of the automaton to a particular
one. We prove that it is a PSPACE-complete problem to check whether the
language of reset words for a given automaton coincides with the language of
reset words for some particular automaton.Comment: 12 pages, 4 figure
Reset thresholds of automata with two cycle lengths
We present several series of synchronizing automata with multiple parameters,
generalizing previously known results. Let p and q be two arbitrary co-prime
positive integers, q > p. We describe reset thresholds of the colorings of
primitive digraphs with exactly one cycle of length p and one cycle of length
q. Also, we study reset thresholds of the colorings of primitive digraphs with
exactly one cycle of length q and two cycles of length p.Comment: 11 pages, 5 figures, submitted to CIAA 201
Limit Synchronization in Markov Decision Processes
Markov decision processes (MDP) are finite-state systems with both strategic
and probabilistic choices. After fixing a strategy, an MDP produces a sequence
of probability distributions over states. The sequence is eventually
synchronizing if the probability mass accumulates in a single state, possibly
in the limit. Precisely, for 0 <= p <= 1 the sequence is p-synchronizing if a
probability distribution in the sequence assigns probability at least p to some
state, and we distinguish three synchronization modes: (i) sure winning if
there exists a strategy that produces a 1-synchronizing sequence; (ii)
almost-sure winning if there exists a strategy that produces a sequence that
is, for all epsilon > 0, a (1-epsilon)-synchronizing sequence; (iii) limit-sure
winning if for all epsilon > 0, there exists a strategy that produces a
(1-epsilon)-synchronizing sequence.
We consider the problem of deciding whether an MDP is sure, almost-sure,
limit-sure winning, and we establish the decidability and optimal complexity
for all modes, as well as the memory requirements for winning strategies. Our
main contributions are as follows: (a) for each winning modes we present
characterizations that give a PSPACE complexity for the decision problems, and
we establish matching PSPACE lower bounds; (b) we show that for sure winning
strategies, exponential memory is sufficient and may be necessary, and that in
general infinite memory is necessary for almost-sure winning, and unbounded
memory is necessary for limit-sure winning; (c) along with our results, we
establish new complexity results for alternating finite automata over a
one-letter alphabet
Application of Photothermal and Photoacoustic Spectroscopy for the Monitoring of Aqueous Dispersions of Carbon Nanomaterials
Photothermal and optoacoustic spectroscopy in their state-of-the-art techniques—multiwavelength, scanning and transient—are used for complex investigation and analysis (chemical analysis and the estimation of physicochemical properties and size) of novel carbon materials—fullerenes and nanodiamonds—and their aqueous dispersions as promising biomedical nanosystems. The estimation of the cluster size and the possibilities to determine subnanogram amounts of both nanodiamonds and fullerenes by these techniques are shown. The comparison of fullerene solutions in various solvents, toluene, N-methylpyrrolydone and water, is made. The advantages of the photothermal and optoacoustic techniques over conventional spectroscopies and the current limitation are discussed. The necessity to develop robust models for transient and imaging photothermal techniques is outlined
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