121 research outputs found
Checking Whether an Automaton Is Monotonic Is NP-complete
An automaton is monotonic if its states can be arranged in a linear order
that is preserved by the action of every letter. We prove that the problem of
deciding whether a given automaton is monotonic is NP-complete. The same result
is obtained for oriented automata, whose states can be arranged in a cyclic
order. Moreover, both problems remain hard under the restriction to binary
input alphabets.Comment: 13 pages, 4 figures. CIAA 2015. The final publication is available at
http://link.springer.com/chapter/10.1007/978-3-319-22360-5_2
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
On the Number of Synchronizing Colorings of Digraphs
We deal with -out-regular directed multigraphs with loops (called simply
\emph{digraphs}). The edges of such a digraph can be colored by elements of
some fixed -element set in such a way that outgoing edges of every vertex
have different colors. Such a coloring corresponds naturally to an automaton.
The road coloring theorem states that every primitive digraph has a
synchronizing coloring.
In the present paper we study how many synchronizing colorings can exist for
a digraph with vertices. We performed an extensive experimental
investigation of digraphs with small number of vertices. This was done by using
our dedicated algorithm exhaustively enumerating all small digraphs. We also
present a series of digraphs whose fraction of synchronizing colorings is equal
to , for every and the number of vertices large enough.
On the basis of our results we state several conjectures and open problems.
In particular, we conjecture that is the smallest possible fraction of
synchronizing colorings, except for a single exceptional example on 6 vertices
for .Comment: CIAA 2015. The final publication is available at
http://link.springer.com/chapter/10.1007/978-3-319-22360-5_1
Large Aperiodic Semigroups
The syntactic complexity of a regular language is the size of its syntactic
semigroup. This semigroup is isomorphic to the transition semigroup of the
minimal deterministic finite automaton accepting the language, that is, to the
semigroup generated by transformations induced by non-empty words on the set of
states of the automaton. In this paper we search for the largest syntactic
semigroup of a star-free language having left quotients; equivalently, we
look for the largest transition semigroup of an aperiodic finite automaton with
states.
We introduce two new aperiodic transition semigroups. The first is generated
by transformations that change only one state; we call such transformations and
resulting semigroups unitary. In particular, we study complete unitary
semigroups which have a special structure, and we show that each maximal
unitary semigroup is complete. For there exists a complete unitary
semigroup that is larger than any aperiodic semigroup known to date.
We then present even larger aperiodic semigroups, generated by
transformations that map a non-empty subset of states to a single state; we
call such transformations and semigroups semiconstant. In particular, we
examine semiconstant tree semigroups which have a structure based on full
binary trees. The semiconstant tree semigroups are at present the best
candidates for largest aperiodic semigroups.
We also prove that is an upper bound on the state complexity of
reversal of star-free languages, and resolve an open problem about a special
case of state complexity of concatenation of star-free languages.Comment: 22 pages, 1 figure, 2 table
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
COD Fractions in Sewage Flowing into Polish Sewage Treatment Plants
The paper presents the results of studies concerning the designation of COD fraction in raw wastewater. The research was conducted in three mechanical-biological sewage treatment plants. The results were compared with data assumed in the ASM models. During the investigation, the following fractions of COD were determined: dissolved non-biodegradable SI, dissolved easily biodegradable SS, in organic suspension slowly degradable XS, and in organic suspension non-biodegradable XI. The methodology fordetermining the COD fraction was based on the ATV- A 131guidelines. The real concentration of fractions in raw wastewater and the percentage of each fraction in total CODare different from data reported in the literature
The fate of nitrogen in the urban area – The case of Zielona Góra, Poland
The anthropogenic change of the nitrogen (N) cycle is strongly triggered by urban demand (such as food and meat consumption, energy demand and transport). As a consequence of high population density, impacts on human health through water and air pollution also concentrate on a city environment. Thus, an urban perspective on a predominantly rural pollution becomes relevant. Urban N budgets may be considered less intrinsically connected, so that separation of an agri-food chain and an industry-combustion chain is warranted. Results have been obtained for Zielona Góra, Poland, a city of 140,000 inhabitants characterized by domestic and transport sources and forest-dominated surroundings. In addition to food imports in Zielona Gora amounting to about 30 %, in the suburban area a significant share of N amounting to 41 % is related to fertilizer imports. The remaining imports are in fuel, electronics, textiles, plastics and paper. Most of the agri-food N (45 %) is denitrified in wastewater treatment. N associated with combustion (mainly NOx emissions from vehicles) represents a much smaller share than N entering via the agri-food system, amounting to 22 % of the total N imports. This overall picture is maintained also when specifically addressing the city center, with the exception of mineral fertilizer that plays a much smaller role, with just 7 % of N imports to the city
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