By Francisco Azevedo

ISBN-10: 058545860X

ISBN-13: 9780585458601

ISBN-10: 1586033042

ISBN-13: 9781586033040

Structures are topic to faults of their elements, affecting their total behaviour. In a "black-box" process, such faults basically develop into obvious within the output whilst applicable inputs are given, which poses a couple of pride and optimization difficulties relating to either trying out and diagnosing. This paintings addresses such difficulties constructing versions with multi-valued logics that it formalizes and generalizes to a number of faults. Such logics expand Boolean good judgment through encoding dependencies on faults, therefore permitting the modelling of an arbitrary variety of diagnostic theories. The effectiveness of constraint fixing over finite domain names and units is proven on a number of difficulties.

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**Extra info for Constraint Solving over Multi-Valued Logics: Application to Digital Circuits**

**Example text**

It consists of a recursive procedure in which the value of a gate output is justified by values of the gate inputs, until Pis are reached. For some values, some gate inputs may be left unspecified since it is enough that one of them takes the controlling value (absorbing element) of the gate. 4. 4. 3 Multi-valued Logics To control error propagation, the composite logic values r/^must be considered. There are four such pairs of values, namely {0/0, 0/1, 1/0, 1/1}. Logic operations between composite logic values can be evaluated by composing the results for the fault-free and faulty circuits.

To avoid carrying on a computation when no more ^-signals are present, it is sufficient to maintain one counter for the current number of ^-signals present in the circuit at any step of the computation. After fault-activation, the program may backtrack as soon as the counter is null. If this heuristic procedure works well in many situations, in others the number of choice points created is too large. Moreover, backtracking on a choice point is caused by the failure of solving a possibly large Boolean CSP.

We may thus infer the global implication Z=l B—1. Nevertheless, such symbolic reasoning implicitly computes all solutions, thus turning a problem such as TG (where the usual goal is to find a solution) into the NP-hard complexity category. 2 CLP(B) - Finite Domain Boolean constraints can be solved more efficiently by a number of incomplete Boolean solvers, obtained as a specialisation of a finite domains solver [Codognet and Diaz 1997]. In [Simonis 1989], the author suggests a technique to generate test patterns for SSFs, implemented in the CLP system CHIP [Dincbas eta/.

### Constraint Solving over Multi-Valued Logics: Application to Digital Circuits by Francisco Azevedo

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