2,459 research outputs found
Some undecidability results concerning the property of preserving regularity
AbstractA finite string-rewriting system R preserves regularity if and only if it preserves Σ-regularity, where Σ is the alphabet containing exactly those letters that have occurrences in the rules of R. This proves a conjecture of Gyenizse and Vágvölgyi (1997). In addition, some undecidability results are presented that generalize results of Gilleron and Tison (1995) from term-rewriting systems to string-rewriting systems. It follows that the property of being regularity preserving is undecidable for term-rewriting systems, thus answering another question of Gyenizse and Vágvölgyi (1997). Finally, it is shown that it is undecidable in general whether a finite, lengthreducing, and confluent string-rewriting system yields a regular set of normal forms for each regular language
Termination of Rewriting with Right-Flat Rules Modulo Permutative Theories
We present decidability results for termination of classes of term rewriting
systems modulo permutative theories. Termination and innermost termination
modulo permutative theories are shown to be decidable for term rewrite systems
(TRS) whose right-hand side terms are restricted to be shallow (variables occur
at depth at most one) and linear (each variable occurs at most once). Innermost
termination modulo permutative theories is also shown to be decidable for
shallow TRS. We first show that a shallow TRS can be transformed into a flat
(only variables and constants occur at depth one) TRS while preserving
termination and innermost termination. The decidability results are then proved
by showing that (a) for right-flat right-linear (flat) TRS, non-termination
(respectively, innermost non-termination) implies non-termination starting from
flat terms, and (b) for right-flat TRS, the existence of non-terminating
derivations starting from a given term is decidable. On the negative side, we
show PSPACE-hardness of termination and innermost termination for shallow
right-linear TRS, and undecidability of termination for flat TRS.Comment: 20 page
A Polynomial Time Algorithm for Deciding Branching Bisimilarity on Totally Normed BPA
Strong bisimilarity on normed BPA is polynomial-time decidable, while weak
bisimilarity on totally normed BPA is NP-hard. It is natural to ask where the
computational complexity of branching bisimilarity on totally normed BPA lies.
This paper confirms that this problem is polynomial-time decidable. To our
knowledge, in the presence of silent transitions, this is the first
bisimilarity checking algorithm on infinite state systems which runs in
polynomial time. This result spots an instance in which branching bisimilarity
and weak bisimilarity are both decidable but lie in different complexity
classes (unless NP=P), which is not known before.
The algorithm takes the partition refinement approach and the final
implementation can be thought of as a generalization of the previous algorithm
of Czerwi\'{n}ski and Lasota. However, unexpectedly, the correctness of the
algorithm cannot be directly generalized from previous works, and the
correctness proof turns out to be subtle. The proof depends on the existence of
a carefully defined refinement operation fitted for our algorithm and the
proposal of elaborately developed techniques, which are quite different from
previous works.Comment: 32 page
non-BPS walls of marginal stability
We explore the properties of non-BPS multi-centre extremal black holes in
ungauged N=2 supergravity coupled to n_v vector multiplets, as described by
solutions to the composite non-BPS linear system. After setting up an explicit
description that allows for arbitrary non-BPS charges to be realised at each
centre, we study the structure of the resulting solutions. Using these results,
we prove that the binding energy of the composite is always positive and we
show explicitly the existence of walls of marginal stability for generic
choices of charges. The two-centre solutions only exist on a hypersurface of
dimension n_v+1 in moduli space, with an n_v-dimensional boundary, where the
distance between the centres diverges and the binding energy vanishes.Comment: 54 pages, 1 figur
On prefixal one-rule string rewrite systems
International audiencePrefixal one-rule string rewrite systems are one-rule string rewrite systems for which the left-hand side of the rule is a prefix of the right-hand side of the rule. String rewrite systems induce a transformation over languages: from a starting word, one can associate all its descendants. We prove, in this work, that the transformation induced by a prefixal one-rule rewrite system always transforms a finite language into a context-free language, a property that is surprisingly not satisfied by arbitrary one-rule rewrite systems. We also give here a decidable characterization of the prefixal one-rule rewrite systems whose induced transformation is a rational transduction
On the descriptional complexity of iterative arrays
The descriptional complexity of iterative arrays (lAs) is studied. Iterative arrays are a parallel computational model with a sequential processing of the input. It is shown that lAs when compared to deterministic finite automata or pushdown automata may provide savings in size which are not bounded by any recursive function, so-called non-recursive trade-offs. Additional non-recursive trade-offs are proven to exist between lAs working in linear time and lAs working in real time. Furthermore, the descriptional complexity of lAs is compared with cellular automata (CAs) and non-recursive trade-offs are proven between two restricted classes. Finally, it is shown that many decidability questions for lAs are undecidable and not semidecidable
Supersymmetric vortex defects in two dimensions
We study codimension-two BPS defects in 2d N=(2,2) supersymmetric gauge
theories, focusing especially on those characterized by vortex-like
singularities in the dynamical or non-dynamical gauge field. We classify
possible SUSY-preserving boundary conditions on charged matter fields around
the vortex defects, and derive a formula for defect correlators on the squashed
sphere. We also prove an equivalence relation between vortex defects and 0d-2d
coupled systems. Our defect correlators are shown to be consistent with the
mirror symmetry duality between Abelian gauged linear sigma models and
Landau-Ginzburg models, as well as that between the minimal model and its
orbifold. We also study the vortex defects inserted at conical singularities.Comment: 67 pages; v2: typos corrected, references added, v3: typos corrected,
references added, a few statements clarified, a minor correction, version to
appear in JHE
Central charges and boundary fields for two dimensional dilatonic black holes
In this paper we first show that within the Hamiltonian description of
general relativity, the central charge of a near horizon asymptotic symmetry
group is zero, and therefore that the entropy of the system cannot be estimated
using Cardy's formula. This is done by mapping a static black hole to a two
dimensional space. We explain how such a charge can only appear to a static
observer who chooses to stay permanently outside the black hole. Then an
alternative argument is given for the presence of a universal central charge.
Finally we suggest an effective quantum theory on the horizon that is
compatible with the thermodynamics behaviour of the black hole.Comment: 16 pages, no figures, LaTex 2e, references adde
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