Expansions, free inverse semigroups, and Schützenberger product

AbstractIn this paper we shall present a new construction of the free inverse monoid on a set X. Contrary to the previous constructions of [9, 11], our construction is symmetric and originates from classical ideas of language theory. The ingredients of this construction are the free group on X and the relation that associates to a word w of the free monoid on X, the set of all pairs (u, v) such that uv = w. It follows at once from our construction that the free inverse monoid on X can be naturally embedded into the Schützenberger product of two free groups of basis X. We shall also give some connections with the theory of expansions as developed by Rhodes and Birget [2, 3]

Most Complex Regular Right-Ideal Languages

A right ideal is a language L over an alphabet A that satisfies L = LA*. We show that there exists a stream (sequence) (R_n : n \ge 3) of regular right ideal languages, where R_n has n left quotients and is most complex under the following measures of complexity: the state complexities of the left quotients, the number of atoms (intersections of complemented and uncomplemented left quotients), the state complexities of the atoms, the size of the syntactic semigroup, the state complexities of the operations of reversal, star, and product, and the state complexities of all binary boolean operations. In that sense, this stream of right ideals is a universal witness.Comment: 19 pages, 4 figures, 1 tabl

From algebra to logic: there and back again -- the story of a hierarchy

This is an extended survey of the results concerning a hierarchy of languages that is tightly connected with the quantifier alternation hierarchy within the two-variable fragment of first order logic of the linear order.Comment: Developments in Language Theory 2014, Ekaterinburg : Russian Federation (2014

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

Synchronizing Random Almost-Group Automata

In this paper we address the question of synchronizing random automata in the critical settings of almost-group automata. Group automata are automata where all letters act as permutations on the set of states, and they are not synchronizing (unless they have one state). In almost-group automata, one of the letters acts as a permutation on $n-1$ states, and the others as permutations. We prove that this small change is enough for automata to become synchronizing with high probability. More precisely, we establish that the probability that a strongly connected almost-group automaton is not synchronizing is $\frac{2^{k-1}-1}{n^{2(k-1)}}(1+o(1))$, for a $k$-letter alphabet.Comment: full version prepared for CIAA 201

Conceptual design of an aircraft automated coating removal system

Paint stripping of the U.S. Air Force`s large transport aircrafts is currently a labor-intensive, manual process. Significant reductions in costs, personnel and turnaround time can be accomplished by the judicious use of automation in some process tasks. This paper presents the conceptual design of a coating removal systems for the tail surfaces of the C-5 plane. Emphasis is placed on the technology selection to optimize human-automation synergy with respect to overall costs, throughput, quality, safety, and reliability. Trade- offs between field-proven vs. research-requiring technologies, and between expected gain vs. cost and complexity, have led to a conceptual design which is semi-autonomous (relying on the human for task specification and disturbance handling) yet incorporates sensor- based automation (for sweep path generation and tracking, surface following, stripping quality control and tape/breach handling)

Grain boundary effects on magnetotransport in bi-epitaxial films of La0.7_{0.7}Sr0.3_{0.3}MnO3_3

The low field magnetotransport of La$_{0.7}$Sr$_{0.3}$MnO$_3$ (LSMO) films grown on SrTiO$_3$ substrates has been investigated. A high qualtity LSMO film exhibits anisotropic magnetoresistance (AMR) and a peak in the magnetoresistance close to the Curie temperature of LSMO. Bi-epitaxial films prepared using a seed layer of MgO and a buffer layer of CeO$_2$ display a resistance dominated by grain boundaries. One film was prepared with seed and buffer layers intact, while a second sample was prepared as a 2D square array of grain boundaries. These films exhibit i) a low temperature tail in the low field magnetoresistance; ii) a magnetoconductance with a constant high field slope; and iii) a comparably large AMR effect. A model based on a two-step tunneling process, including spin-flip tunneling, is discussed and shown to be consistent with the experimental findings of the bi-epitaxial films.Comment: REVTeX style; 14 pages, 9 figures. Figure 1 included in jpeg format (zdf1.jpg); the eps was huge. Accepted to Phys. Rev.

Opacity Issues in Games with Imperfect Information

We study in depth the class of games with opacity condition, which are two-player games with imperfect information in which one of the players only has imperfect information, and where the winning condition relies on the information he has along the play. Those games are relevant for security aspects of computing systems: a play is opaque whenever the player who has imperfect information never "knows" for sure that the current position is one of the distinguished "secret" positions. We study the problems of deciding the existence of a winning strategy for each player, and we call them the opacity-violate problem and the opacity-guarantee problem. Focusing on the player with perfect information is new in the field of games with imperfect-information because when considering classical winning conditions it amounts to solving the underlying perfect-information game. We establish the EXPTIME-completeness of both above-mentioned problems, showing that our winning condition brings a gap of complexity for the player with perfect information, and we exhibit the relevant opacity-verify problem, which noticeably generalizes approaches considered in the literature for opacity analysis in discrete-event systems. In the case of blindfold games, this problem relates to the two initial ones, yielding the determinacy of blindfold games with opacity condition and the PSPACE-completeness of the three problems.Comment: In Proceedings GandALF 2011, arXiv:1106.081

Search for the standard model Higgs boson decaying into two photons in pp collisions at sqrt(s)=7 TeV

A search for a Higgs boson decaying into two photons is described. The analysis is performed using a dataset recorded by the CMS experiment at the LHC from pp collisions at a centre-of-mass energy of 7 TeV, which corresponds to an integrated luminosity of 4.8 inverse femtobarns. Limits are set on the cross section of the standard model Higgs boson decaying to two photons. The expected exclusion limit at 95% confidence level is between 1.4 and 2.4 times the standard model cross section in the mass range between 110 and 150 GeV. The analysis of the data excludes, at 95% confidence level, the standard model Higgs boson decaying into two photons in the mass range 128 to 132 GeV. The largest excess of events above the expected standard model background is observed for a Higgs boson mass hypothesis of 124 GeV with a local significance of 3.1 sigma. The global significance of observing an excess with a local significance greater than 3.1 sigma anywhere in the search range 110-150 GeV is estimated to be 1.8 sigma. More data are required to ascertain the origin of this excess.Comment: Submitted to Physics Letters