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In practice, propositional formulae to describe hardware can be enormous, involving hundreds of thousands of nodes As a result, hardware companies have an interest in smart algorithms to process these formulae and check them for correctness The circuits in the computers you use from day to day have almost certainly been verified using advanced propositional logic techniques, often using a functional language as the means to drive and control the analysis of the circuits A major advance in the application of symbolic techniques to hardware design occurred in the late 1980s with the discovery of binary decision diagrams, a representation for propositional logic formulae that is compact for many common circuit designs BDDs represent a propositional formula via the use of if .. then .. else conditionals alone, which you write as (variable => true-branch | falsebranch).

ave you ever wondered what goes on inside a database system While you may know the basics of a relational database system (RDBS) and be an expert at administering the system, you may have never explored the inner workings of a database system. Most of us have been trained on and have experience with managing database systems, but neither academic nor professional training includes much about the way database systems are constructed. A database professional may never need this knowledge, but it is good to know how the system works so that you can understand how best to optimize your server and even how best to utilize its features. This chapter covers the basics of the subsystems that RDBSs contain and how they are constructed. I use the anatomy of the MySQL system to illustrate the key components of modern RDBSs. For those of you who have studied the inner workings of such systems and want to jump ahead to a look at the architecture of MySQL, you can skip the next section.

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Stream.Begin/EndWrite Socket.BeginAccept/EndAccept Socket.BeginReceive/EndRecevie Socket.BeginSend/EndSend WebRequest.Begin/EndGetResponse

Special nodes are used for true and false at the leaves: you write these as T and F Every BDD is constructed with respect to a global variable ordering, so x AND NOT y can be represented as (x => (y => F | T) | F) if x comes before y in this ordering and as (y => F | (x => T | F)) if y comes before x The variable ordering can be critical for performance of the representation BDDs are efficient because they use some of the language representation techniques you saw in 9 In particular, they work by uniquely memoizing all BDD nodes that are identical, which works by representing a BDD as an integer index into a lookup table that stores the real information about the node.

Although understanding the inner workings of an RDBS isn t necessary for hosting databases or even maintaining the server or developing applications that use the system, knowing how the system is organized is essential to being able to modify and extend its features. It is also important to grasp the basic principles of the most popular database systems to understand how these systems compare to an RDBS.

Furthermore, negative indexes are used to represent the negation of a particular BDD node without creating a separate entry for the negated node Listing 12-15 shows an implementation of BDDs Fully polished BDD packages are often implemented in C It s easy to access those packages from F#.

SqlCommand.Begin/EndExecuteReader SqlCommand.Begin/EndExecuteXmlReader SqlCommand.Begin/EndExecuteNonQuery

Most database professionals work with RDBSs, but several others are becoming popular. The following sections present a brief overview of the three most popular types of database systems: object-oriented, object-relational, and relational. It is important to understand the architectures and general features of these systems to fully appreciate the opportunity that MySQL AB has provided by developing MySQL as open source software and exposing the source code for the system to everyone. This permits me to show you what s going on inside the box. If you are familiar with these types of database systems, you can skip to the Relational Database System Architecture section.

using the techniques described in 19. Here, you have a clear and simple implementation entirely in F# code. Listing 12-15. Implementing Binary Decision Diagrams open System.Collections.Generic let memoize f = let tab = new Dictionary<_,_>() fun x -> if tab.ContainsKey(x) then tab.[x] else let res = f x in tab.[x] <- res; res type type type type BddIndex = int Bdd = Bdd of BddIndex BddNode = Node of Var * BddIndex * BddIndex BddBuilder(order : Var -> Var -> int) =

Execute an SqlCommand asynchronously. Execute a read of XML asynchronously. Execute a nonreading SqlCommand asynchronously.

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