Boolean expression

To determine the minimal cutsets of a fault tree, the tree is first translated into its equivalent Boolean equations and then either the "top-down" or "bottom-up" substitution method is used. The methods are straightforward and involve substituting and expanding Boolean expressions Two Boolean laws, the distributive law and the law of absorption (Table 2.1-1), are used to remove superfluous items. 

Just as there are universal computers that, given a particular input, can simulate any other com-puter, there are NP-complete problems that, with the appropriate input, are effectively equivalent to any NP-hard problem of a given size. For example, Boolean satisfiability -i.e. the problem of determining truth values of the variable s of a Boolean expression so that the expression is true -is known to be an NP-complete problem. See section 12.3.5.2... 

Any connection of extended predicate terms using AND and OR (a and v ) is a Boolean expression. 

If Q is any Boolean expression and and B2 are well-structured subschemas the following can be considered well-structured ... 

We should like to allow the use of arbitrary Boolean expressions in WHILE constructions. This does represent an extension of the power of our programming language. Consider the program scheme P whose graph appears in Example IV-5 in our language P becomes ... 

Hence P is not strongly equivalent to any simple WHILE scheme. Thus allowing arbitrary Boolean expressions in WHILE constructions does indeed extend the power of our language. 

Let us give the construction for block B from Example IV 4 which gave a division of the scheme of Example IV-3 into major blocks. The critical points are a and 8 and the new variables are u(21,a,x ) and u(21,6,x2). The Boolean expression which gives the conditions under which a computation goes from the entry... 

First let us extend the definition of recursion equation as we did the definition of WHILE scheme. Let a Boolean expression be any expression involving predicate terms P(t, ...,tm) where each is a terminal term (not necessarily a variable), and the connectives AND, OR, and NOT. We define a recursion expression inductively, by saying that first any term is a recursion expression, and then that any statement of the form IF Q THEN ELSE E2 is a recursion expression if Q is a Boolean predicate and E and E2 are recursion expressions. 

A wff formed without any application of 2) is quantifier-free. wff containing no usage of " = " is a Boolean expression. 

An invariant is a Boolean expression. The usual Boolean operators (as used in programming languages) are available there are different ways of writing them depending on your preferences. Tables 2.1, 2.2, and 2.3 display them. 

Well-written postconditions can be used as the basis for verification and testing. For this purpose, we should write the postconditions in a more precise style as test (Boolean) functions. You can use the Boolean expression part of your favorite programming language we will use a general syntax from UML called Object Constraint Language (OCL). It translates readily to most programming languages but is more convenient for specification. 

The precondition is also a purely Boolean expression and has no side effects it can refer only to inputs and initial values of attributes. The corresponding postcondition is not guaranteed by the implementor if the precondition did not hold. 

Writing a specification for an operation is very different from writing an implementation. The spec is simply a Boolean expression a relation between the inputs, initial state, final state, and outputs. An implementation would choose a particular algorithmic sequence of steps, select a data representation or specific internal access functions, and work through iterations, branches, and many intermediate states before achieving the final state. Consider the specifications of these operations in contrast to their possible implementations ... 

A state chart can be divided into concurrent sections by a dashed line. Each of these sections is a separate simple state chart. The object is simultaneously in one state from each of the sections. No explicit invariants are needed because the two sets of states are independent. There is no paradox in this, nor necessarily any concurrent processing in the usual sense if s just that a state simply represents a Boolean expression, and there is no reason that two such statements should not be hue at the same time. 

P1 imports P2 is a Boolean expression stating that every statement of P1 can also be found in P2. You can also write P1 => P2. 

Suppose, in some context, you can find a match for both a Boolean expression and its opposite ... 

Boolean Expressions yielding true, false (or unknown). 

The CD-ROM version of the data base can be efficiently searched with a menu-driven type of software called Search Express. It allows one to search with Boolean expressions as well as individual words and/or frequency of hits as a function of the number of documents retrieved on a given topic. Numerous searchable fields have been included, allowing one to retrieve information by a variety of means, for example, the compound name the chemical registry number, the amount of material released into the air, water, or land the location of the site of release and the SIC code of the releasing party. One can also employ ranging methods with available numeric fields and sorting of output. 

EMBL Nucleotide Sequence Database. SWISS-PROT consists of core sequence data with minimal redundancy, citation and extensive annotations including protein function, post-translational modifications, domain sites, protein structural information, diseases associated with protein deficiencies and variants. SWISS-PROT and TrEMBL are available at EBI site, http //www.ebi.ac.uk/swissprot/, and ExPASy site, http //www.expasy.ch/sprot/. From the SWISS-PROT and TrEMBL page of ExPASy site, click Full text search (under Access to SWISS-PROT and TrEMBL) to open the search page (Figure 11.3). Enter the keyword string (use Boolean expression if required), check SWISS-PROT box, and click the Submit button. Select the desired entry from the returned list to view the annotated sequence data in Swiss-Prot format. An output in the fasta format can be requested. Links to BLAST, feature table, some ExPASy proteomic tools (e.g., Compute pI/Mw, ProtParam, ProfileScan, ProtScale, PeptideMass, ScanProsite), and structure (SWISS-MODEL) are provided on the page. 

Thus, a Boolean expression can be written in the following manner for a NAND gate, saying that X = when the complement of (A AND S) = ... 

The more general implications of De Morgan s theorem can be considered after defining two new terms, a dual and a literal. To obtain the dual of a Boolean expression, one must interchange all occurrences of a -t- and a and of a 1 and a 0. A literal is defined as any single variable within the dual expression. For example, in the expression... 

The inverted file is. then, merely a computer application of traditional indexing philosophy. Perhaps the most important difference between computer searching and manual search of a printed index is that the computer enables coordination to be done much more easily at search time. In a computer search, the required term coordinations can be specified, as a Boolean expression for example, much more precisely than could be achieved by any precoordinated indexing system. Computer systems therefore convey a much greater flexibility. 

The definitions of master, bus.active, and cdb handle the process of bus arbitration. We start by selecting an active result register, if one exists, and placing its index in master. We then define the boolean expression bus.active to be true if master indeed points to an active result register. Finally, we define cdb to be this active register. 

In a similar way, the definitions of FUn 5 , and dispatch handle the process of selecting a functional unit and a slot in which the next dispatched instruction should be placed. We consult a table fuJable in order to decide on the functional unit appropriate for dispatching the next instruction pointed to by top, and place its index in FUn- We then select a free slot in the reservation station indexed by FUn- Finally, the boolean expression dispatch is defined to be true if the program has not terminated yet (top < N), and the slot selected is indeed free. 

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