5,353 research outputs found
The tree equivalence of linear recursion schemes
In the paper, a complete system of transformation rules
preserving the tree equivalence and a polynomial-time algorithm
deciding the tree equivalence of linear polyadic recursion
schemes are proposed. The algorithm is formulated as a
sequential transformation process which brings together the
schemes in question. In the last step, the tree equivalence
problem for the given schemes is reduced to a global flow
analysis problem which is solved by an efficient marking
algorithm
Relational semantics of linear logic and higher-order model-checking
In this article, we develop a new and somewhat unexpected connection between
higher-order model-checking and linear logic. Our starting point is the
observation that once embedded in the relational semantics of linear logic, the
Church encoding of any higher-order recursion scheme (HORS) comes together with
a dual Church encoding of an alternating tree automata (ATA) of the same
signature. Moreover, the interaction between the relational interpretations of
the HORS and of the ATA identifies the set of accepting states of the tree
automaton against the infinite tree generated by the recursion scheme. We show
how to extend this result to alternating parity automata (APT) by introducing a
parametric version of the exponential modality of linear logic, capturing the
formal properties of colors (or priorities) in higher-order model-checking. We
show in particular how to reunderstand in this way the type-theoretic approach
to higher-order model-checking developed by Kobayashi and Ong. We briefly
explain in the end of the paper how his analysis driven by linear logic results
in a new and purely semantic proof of decidability of the formulas of the
monadic second-order logic for higher-order recursion schemes.Comment: 24 pages. Submitte
Importance sampling for Lambda-coalescents in the infinitely many sites model
We present and discuss new importance sampling schemes for the approximate
computation of the sample probability of observed genetic types in the
infinitely many sites model from population genetics. More specifically, we
extend the 'classical framework', where genealogies are assumed to be governed
by Kingman's coalescent, to the more general class of Lambda-coalescents and
develop further Hobolth et. al.'s (2008) idea of deriving importance sampling
schemes based on 'compressed genetrees'. The resulting schemes extend earlier
work by Griffiths and Tavar\'e (1994), Stephens and Donnelly (2000), Birkner
and Blath (2008) and Hobolth et. al. (2008). We conclude with a performance
comparison of classical and new schemes for Beta- and Kingman coalescents.Comment: (38 pages, 40 figures
The Diagonal Problem for Higher-Order Recursion Schemes is Decidable
A non-deterministic recursion scheme recognizes a language of finite trees.
This very expressive model can simulate, among others, higher-order pushdown
automata with collapse. We show decidability of the diagonal problem for
schemes. This result has several interesting consequences. In particular, it
gives an algorithm that computes the downward closure of languages of words
recognized by schemes. In turn, this has immediate application to separability
problems and reachability analysis of concurrent systems.Comment: technical report; to appear in LICS'1
Dyson-Schwinger equations in the theory of computation
Following Manin's approach to renormalization in the theory of computation,
we investigate Dyson-Schwinger equations on Hopf algebras, operads and
properads of flow charts, as a way of encoding self-similarity structures in
the theory of algorithms computing primitive and partial recursive functions
and in the halting problem.Comment: 26 pages, LaTeX, final version, in "Feynman Amplitudes, Periods and
Motives", Contemporary Mathematics, AMS 201
Completeness of Flat Coalgebraic Fixpoint Logics
Modal fixpoint logics traditionally play a central role in computer science,
in particular in artificial intelligence and concurrency. The mu-calculus and
its relatives are among the most expressive logics of this type. However,
popular fixpoint logics tend to trade expressivity for simplicity and
readability, and in fact often live within the single variable fragment of the
mu-calculus. The family of such flat fixpoint logics includes, e.g., LTL, CTL,
and the logic of common knowledge. Extending this notion to the generic
semantic framework of coalgebraic logic enables covering a wide range of logics
beyond the standard mu-calculus including, e.g., flat fragments of the graded
mu-calculus and the alternating-time mu-calculus (such as alternating-time
temporal logic ATL), as well as probabilistic and monotone fixpoint logics. We
give a generic proof of completeness of the Kozen-Park axiomatization for such
flat coalgebraic fixpoint logics.Comment: Short version appeared in Proc. 21st International Conference on
Concurrency Theory, CONCUR 2010, Vol. 6269 of Lecture Notes in Computer
Science, Springer, 2010, pp. 524-53
Scott Ranks of Classifications of the Admissibility Equivalence Relation
Let be a recursive language. Let be the set of
-structures with domain . Let be a function with the property that
for all , if and only if
. Then there is some
so that
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