141,681 research outputs found
Disjunctive form and the modal alternation hierarchy
This paper studies the relationship between disjunctive form, a syntactic
normal form for the modal mu calculus, and the alternation hierarchy. First it
shows that all disjunctive formulas which have equivalent tableau have the same
syntactic alternation depth. However, tableau equivalence only preserves
alternation depth for the disjunctive fragment: there are disjunctive formulas
with arbitrarily high alternation depth that are tableau equivalent to
alternation-free non-disjunctive formulas. Conversely, there are
non-disjunctive formulas of arbitrarily high alternation depth that are tableau
equivalent to disjunctive formulas without alternations. This answers
negatively the so far open question of whether disjunctive form preserves
alternation depth. The classes of formulas studied here illustrate a previously
undocumented type of avoidable syntactic complexity which may contribute to our
understanding of why deciding the alternation hierarchy is still an open
problem.Comment: In Proceedings FICS 2015, arXiv:1509.0282
Can Quantum Lattice Fluctuations Destroy the Peierls Broken Symmetry Ground State?
The study of bond alternation in one-dimensional electronic systems has had a
long history. Theoretical work in the 1930s predicted the absence of bond
alternation in the limit of infinitely long conjugated polymers; a result later
contradicted by experimental investigations. When this issue was re-examined in
the 1950s it was shown in the adiabatic limit that bond alternation occurs for
any value of electron-phonon coupling. The question of whether this conclusion
remains valid for quantized nuclear degrees of freedom was first addressed in
the 1980s. Since then a series of numerical calculations on models with gapped,
dispersionless phonons have suggested that bond alternation is destroyed by
quantum fluctuations below a critical value of electron-phonon coupling. In
this work we study a more realistic model with gapless, dispersive phonons. By
solving this model with the DMRG method we show that bond alternation remains
robust for any value of electron-phonon coupling
The \mu-Calculus Alternation Hierarchy Collapses over Structures with Restricted Connectivity
It is known that the alternation hierarchy of least and greatest fixpoint
operators in the mu-calculus is strict. However, the strictness of the
alternation hierarchy does not necessarily carry over when considering
restricted classes of structures. A prominent instance is the class of infinite
words over which the alternation-free fragment is already as expressive as the
full mu-calculus. Our current understanding of when and why the mu-calculus
alternation hierarchy is not strict is limited. This paper makes progress in
answering these questions by showing that the alternation hierarchy of the
mu-calculus collapses to the alternation-free fragment over some classes of
structures, including infinite nested words and finite graphs with feedback
vertex sets of a bounded size. Common to these classes is that the connectivity
between the components in a structure from such a class is restricted in the
sense that the removal of certain vertices from the structure's graph
decomposes it into graphs in which all paths are of finite length. Our collapse
results are obtained in an automata-theoretic setting. They subsume,
generalize, and strengthen several prior results on the expressivity of the
mu-calculus over restricted classes of structures.Comment: In Proceedings GandALF 2012, arXiv:1210.202
Alternation in Quantum Programming: From Superposition of Data to Superposition of Programs
We extract a novel quantum programming paradigm - superposition of programs -
from the design idea of a popular class of quantum algorithms, namely quantum
walk-based algorithms. The generality of this paradigm is guaranteed by the
universality of quantum walks as a computational model. A new quantum
programming language QGCL is then proposed to support the paradigm of
superposition of programs. This language can be seen as a quantum extension of
Dijkstra's GCL (Guarded Command Language). Surprisingly, alternation in GCL
splits into two different notions in the quantum setting: classical alternation
(of quantum programs) and quantum alternation, with the latter being introduced
in QGCL for the first time. Quantum alternation is the key program construct
for realizing the paradigm of superposition of programs.
The denotational semantics of QGCL are defined by introducing a new
mathematical tool called the guarded composition of operator-valued functions.
Then the weakest precondition semantics of QGCL can straightforwardly derived.
Another very useful program construct in realizing the quantum programming
paradigm of superposition of programs, called quantum choice, can be easily
defined in terms of quantum alternation. The relation between quantum choices
and probabilistic choices is clarified through defining the notion of local
variables. We derive a family of algebraic laws for QGCL programs that can be
used in program verification, transformations and compilation. The expressive
power of QGCL is illustrated by several examples where various variants and
generalizations of quantum walks are conveniently expressed using quantum
alternation and quantum choice. We believe that quantum programming with
quantum alternation and choice will play an important role in further
exploiting the power of quantum computing.Comment: arXiv admin note: substantial text overlap with arXiv:1209.437
Dative alternation in Indian English: a corpus-based study
The dative alternation refers to the alternation between two constructions that denote some type of transfer: the double object construction (I give my sister a book) vs. the to-dative construction (I give a book to my sister). We examined the motivations behind the dative alternation in Indian English. A corpus study was performed based on a sample of N = 943 sentences that were drawn from the Kolhapur corpus. Using a mixed-effects logistic regression analysis, we evaluated the effect of 14 predictors that are known to influence the dative alternation in other macro-regional varieties of English. Three predictors were found to be significant: the verb (modeled as a random intercept), the pronominality of the Recipient and the difference in length between the Recipient and the Theme. Our results further corroborate earlier findings that the to-dative construction is more frequently used in Indian English than in other varieties. We argue that the latter tendency may be associated with a transfer from Hindi
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