1,661 research outputs found
Unary patterns under permutations
Thue characterized completely the avoidability of unary patterns. Adding function variables gives a general setting capturing avoidance of powers, avoidance of patterns with palindromes, avoidance of powers under coding, and other questions of recent interest. Unary patterns with permutations have been previously analysed only for lengths up to 3.
Consider a pattern , with , a word variable over an alphabet and function variables, to be replaced by morphic or antimorphic permutations of . If , we show the existence of an infinite word avoiding all pattern instances having . If and all are powers of a single morphic or antimorphic , the length restriction is removed. For the case when is morphic, the length dependency can be removed also for , but not for , as the pattern becomes unavoidable. Thus, in general, the restriction on cannot be removed, even for powers of morphic permutations. Moreover, we show that for every positive integer there exists and a pattern which is unavoidable over all alphabets with at least letters and morphic or antimorphic permutation
Random-bit optimal uniform sampling for rooted planar trees with given sequence of degrees and Applications
In this paper, we redesign and simplify an algorithm due to Remy et al. for
the generation of rooted planar trees that satisfies a given partition of
degrees. This new version is now optimal in terms of random bit complexity, up
to a multiplicative constant. We then apply a natural process
"simulate-guess-and-proof" to analyze the height of a random Motzkin in
function of its frequency of unary nodes. When the number of unary nodes
dominates, we prove some unconventional height phenomenon (i.e. outside the
universal square root behaviour.)Comment: 19 page
The undecidability of joint embedding and joint homomorphism for hereditary graph classes
We prove that the joint embedding property is undecidable for hereditary
graph classes, via a reduction from the tiling problem. The proof is then
adapted to show the undecidability of the joint homomorphism property as well.Comment: 17 pages; DMTCS version; initial version spli
Proof Diagrams for Multiplicative Linear Logic
The original idea of proof nets can be formulated by means of interaction
nets syntax. Additional machinery as switching, jumps and graph connectivity is
needed in order to ensure correspondence between a proof structure and a
correct proof in sequent calculus.
In this paper we give an interpretation of proof nets in the syntax of string
diagrams. Even though we lose standard proof equivalence, our construction
allows to define a framework where soundness and well-typeness of a diagram can
be verified in linear time.Comment: In Proceedings LINEARITY 2016, arXiv:1701.0452
Distributed Processing of Generalized Graph-Pattern Queries in SPARQL 1.1
We propose an efficient and scalable architecture for processing generalized
graph-pattern queries as they are specified by the current W3C recommendation
of the SPARQL 1.1 "Query Language" component. Specifically, the class of
queries we consider consists of sets of SPARQL triple patterns with labeled
property paths. From a relational perspective, this class resolves to
conjunctive queries of relational joins with additional graph-reachability
predicates. For the scalable, i.e., distributed, processing of this kind of
queries over very large RDF collections, we develop a suitable partitioning and
indexing scheme, which allows us to shard the RDF triples over an entire
cluster of compute nodes and to process an incoming SPARQL query over all of
the relevant graph partitions (and thus compute nodes) in parallel. Unlike most
prior works in this field, we specifically aim at the unified optimization and
distributed processing of queries consisting of both relational joins and
graph-reachability predicates. All communication among the compute nodes is
established via a proprietary, asynchronous communication protocol based on the
Message Passing Interface
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