9,659 research outputs found
Satisfiability Games for Branching-Time Logics
The satisfiability problem for branching-time temporal logics like CTL*, CTL
and CTL+ has important applications in program specification and verification.
Their computational complexities are known: CTL* and CTL+ are complete for
doubly exponential time, CTL is complete for single exponential time. Some
decision procedures for these logics are known; they use tree automata,
tableaux or axiom systems. In this paper we present a uniform game-theoretic
framework for the satisfiability problem of these branching-time temporal
logics. We define satisfiability games for the full branching-time temporal
logic CTL* using a high-level definition of winning condition that captures the
essence of well-foundedness of least fixpoint unfoldings. These winning
conditions form formal languages of \omega-words. We analyse which kinds of
deterministic {\omega}-automata are needed in which case in order to recognise
these languages. We then obtain a reduction to the problem of solving parity or
B\"uchi games. The worst-case complexity of the obtained algorithms matches the
known lower bounds for these logics. This approach provides a uniform, yet
complexity-theoretically optimal treatment of satisfiability for branching-time
temporal logics. It separates the use of temporal logic machinery from the use
of automata thus preserving a syntactical relationship between the input
formula and the object that represents satisfiability, i.e. a winning strategy
in a parity or B\"uchi game. The games presented here work on a Fischer-Ladner
closure of the input formula only. Last but not least, the games presented here
come with an attempt at providing tool support for the satisfiability problem
of complex branching-time logics like CTL* and CTL+
Variation in the perception of an L2 contrast : a combined phonetic and phonological account
The present study argues that variation across listeners in the perception of a non-native contrast is due to two factors: the listener-specic weighting of auditory dimensions and the listener-specic construction of new segmental representations. The interaction of both factors is shown to take place in the perception grammar, which can be modelled within an OT framework. These points are illustrated with the acquisition of the Dutch three-member labiodental contrast [V v f] by German learners of Dutch, focussing on four types of learners from the perception study by Hamann and Sennema (2005a)
General Lagrangian Formulation for Higher Spin Fields with Arbitrary Index Symmetry. I. Bosonic fields
We construct a Lagrangian description of irreducible integer higher-spin
representations of the Poincare group with an arbitrary Young tableaux having k
rows, on a basis of the universal BRST approach. Starting with a description of
bosonic mixed-symmetry higher-spin fields in a flat space of any dimension in
terms of an auxiliary Fock space associated with special Poincare module, we
realize a conversion of the initial operator constraint system (constructed
with respect to the relations extracting irreducible Poincare-group
representations) into a first-class constraint system. For this purpose, we
find, for the first time, auxiliary representations of the constraint
subalgebra, to be isomorphic due to Howe duality to sp(2k) algebra, and
containing the subsystem of second-class constraints in terms of new oscillator
variables. We propose a universal procedure of constructing unconstrained
gauge-invariant Lagrangians with reducible gauge symmetries describing the
dynamics of both massless and massive bosonic fields of any spin. It is shown
that the space of BRST cohomologies with a vanishing ghost number is determined
only by the constraints corresponding to an irreducible Poincare-group
representation. As examples of the general procedure, we formulate the method
of Lagrangian construction for bosonic fields subject to arbitrary Young
tableaux having 3 rows and derive the gauge-invariant Lagrangian for new model
of massless rank-4 tensor field with spin and second-stage reducible
gauge symmetries.Comment: 54 pages, abstract, Introduction and Conclusion extended by notes on
new obtained example of Lagrangian for 4-th rank tensor of spin (2,1,1),
Section 6 "Examples" and Appendix D adde
Simple-Current Symmetries, Rank-Level Duality, and Linear Skein Relations for Chern-Simons Graphs
A previously proposed two-step algorithm for calculating the expectation
values of Chern-Simons graphs fails to determine certain crucial signs. The
step which involves calculating tetrahedra by solving certain non- linear
equations is repaired by introducing additional linear equations. As a first
step towards a new algorithm for general graphs we find useful linear equations
for those special graphs which support knots and links. Using the improved set
of equations for tetrahedra we examine the symmetries between tetrahedra
generated by arbitrary simple currents. Along the way we uncover the classical
origin of simple-current charges. The improved skein relations also lead to
exact identities between planar tetrahedra in level and level
CS theories, where denotes a classical group. These results are
recast as identities for quantum -symbols and WZW braid matrices. We obtain
the transformation properties of arbitrary graphs and links under simple
current symmetries and rank-level duality. For links with knotted components
this requires precise control of the braid eigenvalue permutation signs, which
we obtain from plethysm and an explicit expression for the (multiplicity free)
signs, valid for all compact gauge groups and all fusion products.Comment: 58 pages, BRX-TH-30
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