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Enriched $P$-partitions and peak algebras  [PDF]
T. Kyle Petersen
Mathematics , 2005,
Abstract: We develop a more general view of Stembridge's enriched $P$-partitions and use this theory to outline the structure of peak algebras for the symmetric group and the hyperoctahedral group. Initially we focus on commutative peak algebras, spanned by sums of permutations with the same number of peaks, where we consider several variations on the definition of "peak." Whereas Stembridge's enriched $P$-partitions are related to quasisymmetric functions (the dual coalgebra of Solomon's type A descent algebra), our generalized enriched $P$-partitions are related to type B quasisymmetric functions (the dual coalgebra of Solomon's type B descent algebra). Using these functions, we move on to explore (non-commutative) peak algebras spanned by sums of permutations with the same set of peaks. While some of these algebras have been studied before, our approach gives explicit structure constants with a combinatorial description.
On Varieties of Automata Enriched with an Algebraic Structure (Extended Abstract)  [PDF]
Ond?ej Klíma
Computer Science , 2014, DOI: 10.4204/EPTCS.151.3
Abstract: Eilenberg correspondence, based on the concept of syntactic monoids, relates varieties of regular languages with pseudovarieties of finite monoids. Various modifications of this correspondence related more general classes of regular languages with classes of more complex algebraic objects. Such generalized varieties also have natural counterparts formed by classes of finite automata equipped with a certain additional algebraic structure. In this survey, we overview several variants of such varieties of enriched automata.
Human Mobility and Predictability enriched by Social Phenomena Information (extended abstract)  [PDF]
Nicolas Ponieman,Alejo Salles,Carlos Sarraute
Computer Science , 2013,
Abstract: The information collected by mobile phone operators can be considered as the most detailed information on human mobility across a large part of the population. The study of the dynamics of human mobility using the collected geolocations of users, and applying it to predict future users' locations, has been an active field of research in recent years. In this work, we study the extent to which social phenomena are reflected in mobile phone data, focusing in particular in the cases of urban commute and major sports events. We illustrate how these events are reflected in the data, and show how information about the events can be used to improve predictability in a simple model for a mobile phone user's location.
Safer in the Clouds (Extended Abstract)
Chiara Bodei,Viet Dung Dinh,Gian Luigi Ferrari
Electronic Proceedings in Theoretical Computer Science , 2010, DOI: 10.4204/eptcs.38.6
Abstract: We outline the design of a framework for modelling cloud computing systems.The approach is based on a declarative programming model which takes the form of a lambda-calculus enriched with suitable mechanisms to express and enforce application-level security policies governing usages of resources available in the clouds. We will focus on the server side of cloud systems, by adopting a pro-active approach, where explicit security policies regulate server's behaviour.
Abstracting Abstract Control (Extended)  [PDF]
J. Ian Johnson,David Van Horn
Computer Science , 2013, DOI: 10.1145/2661088.2661098
Abstract: The strength of a dynamic language is also its weakness: run-time flexibility comes at the cost of compile-time predictability. Many of the hallmarks of dynamic languages such as closures, continuations, various forms of reflection, and a lack of static types make many programmers rejoice, while compiler writers, tool developers, and verification engineers lament. The dynamism of these features simply confounds statically reasoning about programs that use them. Consequently, static analyses for dynamic languages are few, far between, and seldom sound. The "abstracting abstract machines" (AAM) approach to constructing static analyses has recently been proposed as a method to ameliorate the difficulty of designing analyses for such language features. The approach, so called because it derives a function for the sound and computable approximation of program behavior starting from the abstract machine semantics of a language, provides a viable approach to dynamic language analysis since all that is required is a machine description of the interpreter. The original AAM recipe produces finite state abstractions, which cannot faithfully represent an interpreter's control stack. Recent advances have shown that higher-order programs can be approximated with pushdown systems. However, these automata theoretic models either break down on features that inspect or modify the control stack. In this paper, we tackle the problem of bringing pushdown flow analysis to the domain of dynamic language features. We revise the abstracting abstract machines technique to target the stronger computational model of pushdown systems. In place of automata theory, we use only abstract machines and memoization. As case studies, we show the technique applies to a language with closures, garbage collection, stack-inspection, and first-class composable continuations.
Colored posets and colored quasisymmetric functions  [PDF]
Samuel K. Hsiao,T. Kyle Petersen
Mathematics , 2006,
Abstract: The colored quasisymmetric functions, like the classic quasisymmetric functions, are known to form a Hopf algebra with a natural peak subalgebra. We show how these algebras arise as the image of the algebra of colored posets. To effect this approach we introduce colored analogs of $P$-partitions and enriched $P$-partitions. We also frame our results in terms of Aguiar, Bergeron, and Sottile's theory of combinatorial Hopf algebras and its colored analog.
Categories of Quantum and Classical Channels (extended abstract)  [PDF]
Bob Coecke,Chris Heunen,Aleks Kissinger
Mathematics , 2014, DOI: 10.4204/EPTCS.158.1
Abstract: We introduce the CP*-construction on a dagger compact closed category as a generalisation of Selinger's CPM-construction. While the latter takes a dagger compact closed category and forms its category of "abstract matrix algebras" and completely positive maps, the CP*-construction forms its category of "abstract C*-algebras" and completely positive maps. This analogy is justified by the case of finite-dimensional Hilbert spaces, where the CP*-construction yields the category of finite-dimensional C*-algebras and completely positive maps. The CP*-construction fully embeds Selinger's CPM-construction in such a way that the objects in the image of the embedding can be thought of as "purely quantum" state spaces. It also embeds the category of classical stochastic maps, whose image consists of "purely classical" state spaces. By allowing classical and quantum data to coexist, this provides elegant abstract notions of preparation, measurement, and more general quantum channels.
Computation of unirational fields (extended abstract)  [PDF]
Jaime Gutierrez,David Sevilla
Mathematics , 2008,
Abstract: In this paper we present an algorithm for computing all algebraic intermediate subfields in a separably generated unirational field extension (which in particular includes the zero characteristic case). One of the main tools is Groebner bases theory. Our algorithm also requires computing computing primitive elements and factoring over algebraic extensions. Moreover, the method can be extended to finitely generated K-algebras.
Extended Initiality for Typed Abstract Syntax  [PDF]
Benedikt Ahrens
Computer Science , 2011, DOI: 10.2168/LMCS-8(2:1)2012
Abstract: Initial Semantics aims at interpreting the syntax associated to a signature as the initial object of some category of 'models', yielding induction and recursion principles for abstract syntax. Zsid\'o proves an initiality result for simply-typed syntax: given a signature S, the abstract syntax associated to S constitutes the initial object in a category of models of S in monads. However, the iteration principle her theorem provides only accounts for translations between two languages over a fixed set of object types. We generalize Zsid\'o's notion of model such that object types may vary, yielding a larger category, while preserving initiality of the syntax therein. Thus we obtain an extended initiality theorem for typed abstract syntax, in which translations between terms over different types can be specified via the associated category-theoretic iteration operator as an initial morphism. Our definitions ensure that translations specified via initiality are type-safe, i.e. compatible with the typing in the source and target language in the obvious sense. Our main example is given via the propositions-as-types paradigm: we specify propositions and inference rules of classical and intuitionistic propositional logics through their respective typed signatures. Afterwards we use the category--theoretic iteration operator to specify a double negation translation from the former to the latter. A second example is given by the signature of PCF. For this particular case, we formalize the theorem in the proof assistant Coq. Afterwards we specify, via the category-theoretic iteration operator, translations from PCF to the untyped lambda calculus.
A Formalization and Proof of the Extended Church-Turing Thesis -Extended Abstract-
Nachum Dershowitz,Evgenia Falkovich
Electronic Proceedings in Theoretical Computer Science , 2012, DOI: 10.4204/eptcs.88.6
Abstract: We prove the Extended Church-Turing Thesis: Every effective algorithm can be efficiently simulated by a Turing machine. This is accomplished by emulating an effective algorithm via an abstract state machine, and simulating such an abstract state machine by a random access machine, representing data as a minimal term graph.
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