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He joined the data warehouse team, and after a while, he led the team by taking up the position of a data warehouse architect. Andrey worked mainly with Oracle databases to develop logical and physical models of finance and accounting data, created them in a database, implemented procedures to load and process data, and performed analytical tasks.

He was also responsible for teaching users how to use data warehouse and BI tools, and SQL training was a part of his job as well.

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- Combinatorial Algebra: Syntax and Semantics.
- Combinatorial algebra:syntax and semantics | Mark Sapir.
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After many years of being greatly interested in the aspects of his job that were related to IT rather than accounting or banking, Andrey changed fields. Currently, he works as a database developer in a telecommunication company.

Here, Andrey works mainly with PostgreSQL databases and is responsible for data modeling, implementing data structures in databases, developing stored procedures, integrating databases with other software components, and developing a data warehouse. Having worked with both Oracle and PostgreSQL-the former is a leading commercial and the latter is one of the most advanced open source RDBMSes-he is able to compare them and recognize and evaluate the key advantages of both.

Andrey's extensive experience, therefore, made him able and willing to work on this book. Du kanske gillar. PostgreSQL 9. Spara som favorit. Conjunctive Queries CQ is one of the most basic and studied query languages in database theory, and it corresponds to the primitive positive fragment of first-order logic.

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The evaluation problem for CQs is known to be NP-complete in combined complexity and W[1]-hard in parameterized complexity. However, some syntactic fragments such as acyclic CQs and CQs of bounded tree-width are known to be tractable: CQs from these fragments can be evaluated in polynomial time. A natural optimisation problem is whether a CQ can be rewritten into an equivalent CQ from a tractable fragment.

In this talk I will report on some of the recent advances in this area for classes of acyclic and bounded tree-width CQs and in the presence of data constraints eg, functional dependencies, tgds, etc.

## Combinatorial algebra : syntax and semantics

The language is expressive enough to generate continuous distributions, which raises the question of how to effectively compute in the language. The new semantics demonstrates that it is possible to analyze ProbNetKAT programs precisely using approximations of fixpoints and distributions with finite support. We develop an implementation and show how to solve a variety of practical problems including characterizing the expected performance of traffic engineering schemes based on randomized routing and reasoning probabilistically about properties such as loop freedom.

The starting point of the talk will be the identification of structure common to tree-like combinatorial objects, exemplifying the situation with abstract syntax trees as used in formal languages and with opetopes as used in higher-dimensional algebra. The emerging mathematical structure will be then formalized in a categorical setting, unifying the algebraic aspects of the theory of abstract syntax of [2,3] and the theory of opetopes of [5].

This realization conceptually allows one to transport viewpoints between these, now bridged, mathematical theories and I will explore it here in the direction of higher-dimensional algebra, giving an algebraic combinatorial framework for a generalisation of the slice construction of [1] for generating opetopes.

## Coq Package Index | The Coq Proof Assistant

The technical work will involve setting up a microcosm principle for near-semirings and subsequently exploiting it in the cartesian closed bicategory of generalised species of structures [4]. We relate two contrasting approaches to randomness. Algorithmic randomness classifies infinite sequences as random if they pass a collection of randomness tests specified in computability-theoretic terms. An alternative point-free approach considers instead a generalised space a locale of random sequences, which is non-trivial even though, in this approach, individual random sequences do not exist the locale has no points.

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To connect the two, we give a constructive presentation of the point-free approach, and interpret it in Hyland's effective topos Eff. In Eff, generalised spaces of random sequences characterise, via their classical points, notions of algorithmically random sequence. Categorical compositional distributional semantics is a model of natural language, which combines the statistical vector space models of words with the compositional models of grammar.

We formalise in this model the generalised quantifier theory of natural language, due to Barwise and Cooper. The underlying setting is a compact closed category with bialgebras. We start from a generative grammar formalisation and develop an abstract categorical compositional semantics for it, then instantiate the abstract setting to sets and relations and to finite dimensional vector spaces and linear maps. We prove the equivalence of the relational instantiation to the truth theoretic semantics of generalized quantifiers.

The vector space instantiation formalises the statistical usages of words and enables us to, for the first time, reason about quantified phrases, sentences compositionally, and quantifier scope in distributional semantics. MV-algebras are algebraic structures that arose from Lukasiewicz many-valued logics in the s. They form a rich branch of mathematics, from work of D.

The related area of Effect Algebras arose independently in the s, in quantum measurement and quantum probability theory. Both subjects have come under increasing investigation by categorists using duality theory and monadic methods. In a different direction, recently M.

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Lawson and P. In a distributed game we imagine a team Player engaging a team Opponent in a distributed fashion. Such games and their strategies have been formalised within event structures.

However there are limitations in founding strategies on traditional event structures. Sometimes a probabilistic distributed strategy relies on certain benign races where, intuitively, several members of team Player may race each other to make a common move. Although there are event structures which support such parallel causes, in which an event is enabled in several compatible ways, they do not support an operation of hiding central to the composition of strategies; nor do they support probability adequately.

An extension of traditional event structures is devised which supports parallel causes and hiding, as well as the mix of probability and nondeterminism needed to account for probabilistic distributed strategies. The extension is tested in the construction of a bicategory of probabilistic distributed strategies with parallel causes. We see that similar phenomena arise for finite probabilistic choice and for unbounded nondeterminism.

Consider increment program inc x inc x , where inc x increments x atomically. It is difficult to show that, with pre-condition stating that the value of the counter is 0, the post-condition states that the value of the counter is 2. However, this work is not compositional since more threads require more auxilary variables.