Boolean structuring

Whilst a single residual may be sufficient to detect faults, a vector of residuals is usually required for fault isolation. For isolation purposes, structured residuals [8, 17] can be generated, i.e., each residual is affected only by a specific subset of faults, and each fault only affects a specific subset of residuals. This concept can be expressed in a mathematical form by introducing a boolean fault code vector and a boolean structure matrix [8],... 

The mass balance equation (7.136) leads to a large system of nonlinear algebraic equations. Thanks to the aforementioned clustering procedure, the dimensions of the overall system are conveniently reduced and become Nc x Ns- Figure 7.2 shows a typical Boolean structure of the whole matrix system for a simple structured 2D grid, as well as the structure of a single block. 

You have boolean optimization turned on. Again, this is appropriate only for random logic. If you do have random logic in your design, consider grouping it into a separate level of hierarchy and compile it separately with the flatten or boolean structuring switch turned on. 

Boolean models where the failure of the system is expressed using the Boolean structure function ... 

Other approaches deal with the problem of automatically removing existing loops in fault trees. In (Ciarambino, di Torino, Contini, Demichela, Piccinini 2002), syntax rules are used to identify and remove loops. In (Domis Trapp 2008) Boolean structures are analyzed and loops are removed from the safety analysis model. However, these type of approaches require prior recognition by the analyst of the initiation of a loop. To enable automations for fault tree structures that do not require interactions... 

ENTITY BOOLEAN = STRUCTURE operator first operand second operand END ... 

The Web-based graphical user interface permits a choice from numerous criteria and the performance of rapid searches. This service, based on the chemistry information toolkit CACTVS, provides complex Boolean searches. Flexible substructure searches have also been implemented. Users can conduct 3D pharmacophore queries in up to 25 conformations pre-calculated for each compound. Numerous output formats as well as 2D and 3D visuaHzation options are supplied. It is possible to export search results in various forms and with choices for data contents in the exported files, for structure sets ranging in size from a single compound to the entire database. Additional information and down-loadable files (in various formats) can be obtained from this service. 

Structural keys describe the chemical composition and structural motifs of molecules represented as a Boolean array. If a certain structural feature is present in a molecule or a substructure, a particular bit is set to 1 (true), otherwise to 0 (false). A bit in this array may encode a particular functional group (such as a carboxylic acid or an amidelinkage), a structural element (e.g., a substituted cyclohexane), or at least n occurrences of a particular element (e.g., a carbon atom). Alternatively, the structural key can be defined as an array of integers where the elements of this array contain the frequency of a specific feature in the molecule. 

The logical structure of a fault tree can be described in terms of boolean algebraic equations. Some specific prerequisites to the application of this methodology are as follows. 

Chapter 8 describes a number of generalized CA models, including reversible CA, coupled-map lattices, quantum CA, reaction-diffusion models, immunologically motivated CA models, random Boolean networks, sandpile models (in the context of self-organized criticality), structurally dynamic CA (in which the temporal evolution of the value of individual sites of a lattice are dynamically linked to an evolving lattice structure), and simple CA models of combat. 

Since we will be dealing with finite graphs, we can analyze the behavior of random Boolean nets in the familiar fashion of looking at their attractor (or cycle) state structure. Specifically, we choose to look at (1) the number of attractor state cycles, (2) the average cyclic state length, (3) the sizes of the basins of attraction, (4) the stability of attractors with respect to minimal perturbations, and (4) the changes in the attractor states and basins of attraction induced by mutations in the lattice structure and/or the set of Boolean rules. 

Figure 8.16 shows a portion of typical N, l)-net. The arrows indicate inputs to given sites and + and represent the two active Boolean functions at the sites toward which the arrows are pointing. Note that the structure degenerates into subnets of dynamically independent loops with outwmdly radiating tails . An input signal cannot enter a loop since the site by which it would enter the loop... 

Forcing Structures Consider the Boolean OR function. Note that the value of cti or CT2 is fixed as 1 whenever either a or C2 is equal to 1. Kauffman calls any function with the property that at least one value of at least one of its inputs fixes its output, a canalizing function [kauff84]. The Boolean functions OR and AND , for example, are both canalizing functions, but the EXCLUSIVE OR function is not. 

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

States are often drawn in a state chart showing the states and the relationships between them, as in Figure 3.21. Each state is a Boolean attribute17 an object either is or is not in that state at any time. The structure of states in the state chart defines invariants across these attributes. 

UML has three distinct constructs that remain largely unrelated to one another an attribute, a role in an association, and a state in a state chart. For example, a pie- and postcondition pair cannot refer to the name of a state. In Catalysis these three constructs are closely related. An association defines a pair of inverse attributes that are drawn differently a state defines a Boolean attribute, and the structure of states in a state chart defines invariants on those attributes. Transitions on a state diagram are thus no more than a graphical depiction of action specifications. This approach provides a simpler core set of constructs with different presentations. Actions on UML state transitions are imperative and appear unrelated to pre- and postspecification of operations. 

Since the systems of equations to be considered are quite large, it is necessary to use some compact method to represent the information flow among them. A very convenient technique is to relate the system equations to a digraph and its associated Boolean matrix, which represent the structure of the information flow in the system. The Boolean matrix to be used is called the occurrence matrix (HI, S3), and is defind as follows (1) each row of the occurrence matrix corresponds to a system equation, and each column corresponds to a system variable (2) an element of the matrix, s -, is either a Boolean 1 or 0 according to the rule... 

The rule structure allows simple Boolean functions to be performed. Multiple numbered IF clauses are logically ANDed together. Multiple clauses which are part of the same numbered IF are logically ORed. The logical NOT does not exist, but can be simulated using predicates with the opposite meaning in the IF clause, (i.e. BIGGER is equivalent to NOT SMALLER). Table IV lists the currently available predicates for IF clauses. 

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