16,813 research outputs found
Random Operator Approach for Word Enumeration in Braid Groups
We investigate analytically the problem of enumeration of nonequivalent
primitive words in the braid group B_n for n >> 1 by analysing the random word
statistics and the target space on the basis of the locally free group
approximation. We develop a "symbolic dynamics" method for exact word
enumeration in locally free groups and bring arguments in support of the
conjecture that the number of very long primitive words in the braid group is
not sensitive to the precise local commutation relations. We consider the
connection of these problems with the conventional random operator theory,
localization phenomena and statistics of systems with quenched disorder. Also
we discuss the relation of the particular problems of random operator theory to
the theory of modular functionsComment: 36 pages, LaTeX, 4 separated Postscript figures, submitted to Nucl.
Phys. B [PM
Taming Numbers and Durations in the Model Checking Integrated Planning System
The Model Checking Integrated Planning System (MIPS) is a temporal least
commitment heuristic search planner based on a flexible object-oriented
workbench architecture. Its design clearly separates explicit and symbolic
directed exploration algorithms from the set of on-line and off-line computed
estimates and associated data structures. MIPS has shown distinguished
performance in the last two international planning competitions. In the last
event the description language was extended from pure propositional planning to
include numerical state variables, action durations, and plan quality objective
functions. Plans were no longer sequences of actions but time-stamped
schedules. As a participant of the fully automated track of the competition,
MIPS has proven to be a general system; in each track and every benchmark
domain it efficiently computed plans of remarkable quality. This article
introduces and analyzes the most important algorithmic novelties that were
necessary to tackle the new layers of expressiveness in the benchmark problems
and to achieve a high level of performance. The extensions include critical
path analysis of sequentially generated plans to generate corresponding optimal
parallel plans. The linear time algorithm to compute the parallel plan bypasses
known NP hardness results for partial ordering by scheduling plans with respect
to the set of actions and the imposed precedence relations. The efficiency of
this algorithm also allows us to improve the exploration guidance: for each
encountered planning state the corresponding approximate sequential plan is
scheduled. One major strength of MIPS is its static analysis phase that grounds
and simplifies parameterized predicates, functions and operators, that infers
knowledge to minimize the state description length, and that detects domain
object symmetries. The latter aspect is analyzed in detail. MIPS has been
developed to serve as a complete and optimal state space planner, with
admissible estimates, exploration engines and branching cuts. In the
competition version, however, certain performance compromises had to be made,
including floating point arithmetic, weighted heuristic search exploration
according to an inadmissible estimate and parameterized optimization
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