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

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 $n$ left quotients; equivalently, we look for the largest transition semigroup of an aperiodic finite automaton with $n$ 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 $n \ge 4$ 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 $2^n-1$ 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

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 $k$-out-regular directed multigraphs with loops (called simply \emph{digraphs}). The edges of such a digraph can be colored by elements of some fixed $k$-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 $n$ 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 $1-1/k^d$, for every $d \ge 1$ 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 $1-1/k$ is the smallest possible fraction of synchronizing colorings, except for a single exceptional example on 6 vertices for $k=2$.Comment: CIAA 2015. The final publication is available at http://link.springer.com/chapter/10.1007/978-3-319-22360-5_1

The use of high-dose immunoglobulin M-enriched human immunoglobulin in dogs with immune-mediated hemolytic anemia.

BACKGROUND: The IV use of human immunoglobulin (hIVIG) in dogs with primary immune-mediated hemolytic anemia (IMHA) has been described previously, but herein we describe the use of high-dose IgM-enriched hIVIG (Pentaglobin). HYPOTHESIS/OBJECTIVES: Dogs treated with high-dose Pentaglobin will experience shorter time to remission and hospital discharge and have decreased transfusion requirements compared to dogs receiving standard treatment alone. ANIMALS: Fourteen client-owned dogs diagnosed with primary IMHA at specialist referral hospitals in the United Kingdom. METHODS: All prospectively enrolled dogs received prednisolone, dexamethasone or both along with clopidogrel. Patients were randomized to receive Pentaglobin at 1 g/kg on up to 2 occasions, or to serve as controls. No additional immunosuppressive drugs were allowed within the first 7 days of treatment. Remission was defined as stable PCV for 24 hours followed by an increase in PCV. RESULTS: Ten of 11 dogs from the treatment group and 2 of 3 dogs from the control group achieved remission and survived until hospital discharge. Survival and time to remission were not significantly different between groups. The volume of packed red blood cells transfused, normalized for body weight, was not significantly different between groups. Potential adverse reactions to Pentaglobin occurred in 2 dogs, but their clinical signs may have been related to the underlying disease. CONCLUSIONS AND CLINICAL IMPORTANCE: Treatment with high-dose Pentaglobin was well tolerated by dogs with primary IMHA but no significant advantage was found in this small study. Additional studies examining larger groups and subpopulations of dogs with primary IMHA associated with a poorer prognosis are warranted

Continuous selections of multivalued mappings

This survey covers in our opinion the most important results in the theory of continuous selections of multivalued mappings (approximately) from 2002 through 2012. It extends and continues our previous such survey which appeared in Recent Progress in General Topology, II, which was published in 2002. In comparison, our present survey considers more restricted and specific areas of mathematics. Note that we do not consider the theory of selectors (i.e. continuous choices of elements from subsets of topological spaces) since this topics is covered by another survey in this volume

Emissions from mechanically-biologically treated waste landfills at field scale

Modern waste management tends towards greater sustainability in landfilling, with the implementation of strategies such as the pretreatment of solid waste. This work assesses the behaviour of rejects from a refining stage of mechanically-biologically treated municipal solid waste at the landfill. The main results of 18 months' monitoring of an experimental pilot cell with waste from a full-scale plant are presented. This first stages are expected to be the most problematic period for this type of waste. The evolution of the temperature and the composition of leachate and gas at various points within the cell are included. During the first weeks, pollutant concentrations in the leachate exceeded the reference ranges in the literature, coinciding with a rapid onset of methanogenic conditions. However, there was a quick wash, reducing concentrations to below one third of the initial values before the first year. pH values influenced concentrations of some pollutants such as copper. These results indicate that, right from the beginning of disposal, such facilities should be prepared to treat a high pollution load in the leachate and install the gas emissions control elements due to the rapid onset of methanogenesis.This work is funded by the Spanish Ministry of Economics and Competitiveness through the CTM2012-35055 project. The project is financed jointly by the European Regional Development Fund, FEDER (operational period 2007-2013). The authors wish to thank the Government of Cantabria, through the public company MARE, and TirCantabria, the landfill operator company, for their collaboration