9,103 research outputs found
The First-Order Theory of Ground Tree Rewrite Graphs
We prove that the complexity of the uniform first-order theory of ground tree
rewrite graphs is in ATIME(2^{2^{poly(n)}},O(n)). Providing a matching lower
bound, we show that there is some fixed ground tree rewrite graph whose
first-order theory is hard for ATIME(2^{2^{poly(n)}},poly(n)) with respect to
logspace reductions. Finally, we prove that there exists a fixed ground tree
rewrite graph together with a single unary predicate in form of a regular tree
language such that the resulting structure has a non-elementary first-order
theory.Comment: accepted for Logical Methods in Computer Scienc
Equally-distant partially-entangled alphabet states for quantum channels
Each Bell state has the property that by performing just local operations on
one qubit, the complete Bell basis can be generated. That is, states generated
by local operations are totally distinguishable. This remarkable property is
due to maximal quantum entanglement between the two particles. We present a set
of local unitary transformations that generate out of partially entangled
two-qubit state a set of four maximally distinguishable states that are
mutually equally distant. We discuss quantum dense coding based on these
alphabet states.Comment: 7 revtex pages, 2 eps figures, to appear in Phys. Rev. A 62, 1
November (2000
Deciding regular grammar logics with converse through first-order logic
We provide a simple translation of the satisfiability problem for regular
grammar logics with converse into GF2, which is the intersection of the guarded
fragment and the 2-variable fragment of first-order logic. This translation is
theoretically interesting because it translates modal logics with certain frame
conditions into first-order logic, without explicitly expressing the frame
conditions.
A consequence of the translation is that the general satisfiability problem
for regular grammar logics with converse is in EXPTIME. This extends a previous
result of the first author for grammar logics without converse. Using the same
method, we show how some other modal logics can be naturally translated into
GF2, including nominal tense logics and intuitionistic logic.
In our view, the results in this paper show that the natural first-order
fragment corresponding to regular grammar logics is simply GF2 without extra
machinery such as fixed point-operators.Comment: 34 page
Transducers from Rewrite Rules with Backreferences
Context sensitive rewrite rules have been widely used in several areas of
natural language processing, including syntax, morphology, phonology and speech
processing. Kaplan and Kay, Karttunen, and Mohri & Sproat have given various
algorithms to compile such rewrite rules into finite-state transducers. The
present paper extends this work by allowing a limited form of backreferencing
in such rules. The explicit use of backreferencing leads to more elegant and
general solutions.Comment: 8 pages, EACL 1999 Berge
Algebras with Operator and Campbell--Hausdorff Formula
We introduce some new classes of algebras and estabilish in these algebras
Campbell--Hausdorff like formula. We describe the application of these
constructions to the problem of the connectivity of the Feynman graphs
corresponding to the Green functions in Quantum Fields Theory.Comment: 12 page
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