Linear Parsing Expression Grammars

PEGs were formalized by Ford in 2004, and have several pragmatic operators (such as ordered choice and unlimited lookahead) for better expressing modern programming language syntax. Since these operators are not explicitly defined in the classic formal language theory, it is significant and still challenging to argue PEGs' expressiveness in the context of formal language theory.Since PEGs are relatively new, there are several unsolved problems.One of the problems is revealing a subclass of PEGs that is equivalent to DFAs. This allows application of some techniques from the theory of regular grammar to PEGs. In this paper, we define Linear PEGs (LPEGs), a subclass of PEGs that is equivalent to DFAs. Surprisingly, LPEGs are formalized by only excluding some patterns of recursive nonterminal in PEGs, and include the full set of ordered choice, unlimited lookahead, and greedy repetition, which are characteristic of PEGs. Although the conversion judgement of parsing expressions into DFAs is undecidable in general, the formalism of LPEGs allows for a syntactical judgement of parsing expressions.Comment: Parsing expression grammars, Boolean finite automata, Packrat parsin

Stability and Complexity of Minimising Probabilistic Automata

We consider the state-minimisation problem for weighted and probabilistic automata. We provide a numerically stable polynomial-time minimisation algorithm for weighted automata, with guaranteed bounds on the numerical error when run with floating-point arithmetic. Our algorithm can also be used for "lossy" minimisation with bounded error. We show an application in image compression. In the second part of the paper we study the complexity of the minimisation problem for probabilistic automata. We prove that the problem is NP-hard and in PSPACE, improving a recent EXPTIME-result.Comment: This is the full version of an ICALP'14 pape

Brzozowski Algorithm Is Generically Super-Polynomial Deterministic Automata

International audienceWe study the number of states of the minimal automaton of the mirror of a rational language recognized by a random deterministic automaton with n states. We prove that, for any d > 0, the probability that this number of states is greater than nd tends to 1 as n tends to infinity. As a consequence, the generic and average complexities of Brzozowski minimization algorithm are super-polynomial for the uniform distribution on deterministic automata

Synchronization Problems in Automata without Non-trivial Cycles

We study the computational complexity of various problems related to synchronization of weakly acyclic automata, a subclass of widely studied aperiodic automata. We provide upper and lower bounds on the length of a shortest word synchronizing a weakly acyclic automaton or, more generally, a subset of its states, and show that the problem of approximating this length is hard. We investigate the complexity of finding a synchronizing set of states of maximum size. We also show inapproximability of the problem of computing the rank of a subset of states in a binary weakly acyclic automaton and prove that several problems related to recognizing a synchronizing subset of states in such automata are NP-complete.Comment: Extended and corrected version, including arXiv:1608.00889. Conference version was published at CIAA 2017, LNCS vol. 10329, pages 188-200, 201

Bound and free atoms diagnosed by the recoil-induced resonances: 1D optical lattice in a working MOT

We report on studies of simultaneous trapping of $^{85}$Rb atoms in a magneto-optical trap (MOT) and 1D optical lattice. Using Raman pump-probe spectroscopy we observe the coexistence of two atomic fractions: the first, which consists of free, unbound atoms trapped in a MOT and the second, localized in the micropotentials of the optical lattice. We show that recoil-induced resonances allow not only temperature determination of the atomic cloud but, together with vibrational resonances, can also be used for real-time, nondestructive studies of the lattice loading and of the dynamics of systems comprising unbound and bound atomic fractions.Comment: 6 pages, 7 figures, submitted to PR

Regular Expressions and Transducers over Alphabet-invariant and User-defined Labels

We are interested in regular expressions and transducers that represent word relations in an alphabet-invariant way---for example, the set of all word pairs u,v where v is a prefix of u independently of what the alphabet is. Current software systems of formal language objects do not have a mechanism to define such objects. We define transducers in which transition labels involve what we call set specifications, some of which are alphabet invariant. In fact, we give a more broad definition of automata-type objects, called labelled graphs, where each transition label can be any string, as long as that string represents a subset of a certain monoid. Then, the behaviour of the labelled graph is a subset of that monoid. We do the same for regular expressions. We obtain extensions of a few classic algorithmic constructions on ordinary regular expressions and transducers at the broad level of labelled graphs and in such a way that the computational efficiency of the extended constructions is not sacrificed. For regular expressions with set specs we obtain the corresponding partial derivative automata. For transducers with set specs we obtain further algorithms that can be applied to questions about independent regular languages, in particular the witness version of the independent property satisfaction question

A Kleene theorem for polynomial coalgebras

For polynomial functors G, we show how to generalize the classical notion of regular expression to G-coalgebras. We introduce a language of expressions for describing elements of the final G-coalgebra and, analogously to Kleene’s theorem, we show the correspondence between expressions and finite G-coalgebras

An Automated System for Hydroxide Catalysis Bonding of Precision-Aligned Optical Systems

Precision-aligned, robust, ultra-stable optical assemblies are required in an increasing number of space-based applications such as fundamental science, metrology and geodesy. Hydroxide catalysis bonding is a proven, glue-free, technology for building such optical systems from materials such as ULE, Zerodur and fused silica. Hydroxide catalysis bonded optical systems have flown in missions such as GP-B and LISA Pathfinder achieving picometer path-length stability and microradian component stability over full mission lifetime. Component alignment and bonding was previously a largely manual process that required skilled operators and significant time. We have recently automated most of the alignment and bonding steps with the goals of improving overall precision, speed and reliability. Positioning and bonding of an optical component to within 4 microns and 10 microradians of a target position and alignment can now be reliably completed within half an hour, compared to the many hours typically taken previously. The key new features of this system are an interferometer that monitors the parallelism and separation of the surfaces to be bonded and a precision multi-axis manipulator that can optimise component alignment as it brings it down to the point of bonding. We present a description of the system and a summary of the alignment results obtained in a series of 9 test bonds. We also show how this system is being developed for integration into a precision optical manufacturing facility for assembly of large optical systems

HIV/AIDS among Inmates of and Releasees from US Correctional Facilities, 2006: Declining Share of Epidemic but Persistent Public Health Opportunity

Because certain groups at high risk for HIV/AIDS (human immunodeficiency virus/acquired immunodeficiency syndrome) come together in correctional facilities, seroprevalence was high early in the epidemic. The share of the HIV/AIDS epidemic borne by inmates of and persons released from jails and prisons in the United States (US) in 1997 was estimated in a previous paper. While the number of inmates and releasees has risen, their HIV seroprevalence rates have fallen. We sought to determine if the share of HIV/AIDS borne by inmates and releasees in the US decreased between 1997 and 2006. We created a new model of population flow in and out of correctional facilities to estimate the number of persons released in 1997 and 2006. In 1997, approximately one in five of all HIV-infected Americans was among the 7.3 million who left a correctional facility that year. Nine years later, only one in seven (14%) of infected Americans was among the 9.1 million leaving, a 29.3% decline in the share. For black and Hispanic males, two demographic groups with heightened incarceration rates, recently released inmates comprise roughly one in five of those groups' total HIV-infected persons, a figure similar to the proportion borne by the correctional population as a whole in 1997. Decreasing HIV seroprevalence among those admitted to jails and prisons, prolonged survival and aging of the US population with HIV/AIDS beyond the crime-prone years, and success with discharge planning programs targeting HIV-infected prisoners could explain the declining concentration of the epidemic among correctional populations. Meanwhile, the number of persons with HIV/AIDS leaving correctional facilities remains virtually identical. Jails and prisons continue to be potent targets for public health interventions. The fluid nature of incarcerated populations ensures that effective interventions will be felt not only in correctional facilities but also in communities to which releasees return

Position Automaton Construction for Regular Expressions with Intersection

Positions and derivatives are two essential notions in the conversion methods from regular expressions to equivalent finite automata. Partial derivative based methods have recently been extended to regular expressions with intersection. In this paper, we present a position automaton construction for those expressions. This construction generalizes the notion of position making it compatible with intersection. The resulting automaton is homogeneous and has the partial derivative automaton as its quotient