Constraint graph model

Conflict resolution, relative scheduling, relative control synthesis and optimization are formulated on a constraint graph model that is derived from the sequencing graph model under detailed timing constraints. Descriptions and analyses of these formulations are presented in subsequent chapters. 

This chapter is organized as follows. Section 4.1 describes the semantics of the sequencing graph model. Section 4.2 describes the derivation of a constraint graph model from a sequencing graph model under timing constraints. 

Table 4.3 Edge types in the constraint graph model.

Figure 4.8 The constraint graph model for the encoder process of the Error correcting code example.

The sequencing graph model is the underlying representation for design space exploration, which is described in the next chapter. Relative scheduling, constrained conflict resolution, and relative control synthesis and optimization are all formulated based on the constraint graph model. 

Organization of chapter. This chapter presents the formulation and algorithms for relative scheduling. Our approach can be described in a nutshell as follows. In relative scheduling, we support both operations with fixed delay and operations with data-dependent delay data-dependent delay operations represent points of synchronization. We uniformly model both types of operations as vertices in the constraint graph model. We assume in this cluq)ter that resource binding and conflict resolution have been performed prior to scheduling. 

Finding the set of offsets is identical to scheduling Ga(Va, Ef), where the constraint graph models both operation dependencies and timing constraints. If no such set exists, then the constraints are said to be inconsistent. Since the execution delay of a data-dependent delay vertex can be any integer greater than or equal to zero, a minimum offset o o(fi) is the minimum time after the completion of the anchor a before t)< can begin execution. 

We consider in the rest of this chapter a single constraint graph model G that is derived from a sequencing graph with timing constraints, wh e conflict resolution has been performed on all graphs in its cf-hierarchy G. Therefore, the term instance operation set in the sequel refers to the candidate operation set of with respect to G. 

The objective in conflict resolution is to resolve the conflicts among elements of a candidate operation set 0(t,)(G), which is derived from a resource binding / and a constraint graph model G V, E). An ordering of the instance operation set is defined as follows. 

To define the cost function that will drive the control optimization, we briefly outine the mapping from a constraint graph model of hardware behavior to a control implementation. The details are presented in Chapters 6 and 8 we summarize in this section the major results as background for defining the control optimization criterion. 

In this article we present the constraint graph representation used by MC-SYM to transform structural data into three-dimensional models. Then, we discuss the sequence-structure relation and the theory of possibility to assign plausibility coefficients to each structural hypothesis. Finally, we discuss the application of this technique to the lead-activated riboz5one and indicate how modeling was used iteratively with experimentation to derive its active structure. 

GRAPH 11.33 Two-dimensional Formal Graphs of the constraint that models the spatial damping as a three-dimensional oscillator in electrodynamics. The constraint comes from the existence of an extra capacitance between the electric displacement ( electrization ) D and the potential density V,A-... 

The determination of ARRs on a bond graph model is done by elimination of unknown variables contained in the structural constraints of junctions 0 and 1. The equations of power balance on the junctions constitute the ARRs [16]. 

A diagnosis procedure based on evaluation of physical constraint laws derived from bond graph models is described here. Symbolically written constraints, called analytical redundancy relations (ARRs), are expressed in terms of known variables (measurements and inputs). ARRs are static or dynamic constraints which link the time evolution of the known variables when a system operates according to its normal operation model. The error or deviation from the constraint model is called a residual. The objective of quantitative diagnosis is to evaluate the residuals and associate the fault symptoms with deviations of residuals. 

The process of deriving constraints or ARRs is based on inversion of sensor causalities, i.e., the measurements which are outputs in a normal bond graph model used for simulation become inputs to the constraint model used for diagnosis, i.e., the inputs to the diagnosis model are the measured signals from the actual plant. New virtual sensors are added to the diagnosis model to extract residuals as its outputs [3,4]. In essence, diagnosis is a look-back simulation. 

The input to the structural synthesis phase consists of a sequencing graph model of the hardware behavior to synthesize, along with the following constraints, which can either be specified in the input hardware description, or entered in-tCTactively by the designs. 

The input to Hebe consists of a sequencing graph model and the following constraints ... 

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