1,674 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
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
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