On The Complexity Of The Evaluation Of Transient Extensions Of Boolean Functions

Electronic version of an article published as International Journal of Foundations of Computer Science, 23(01), 2012, 21–35. http://dx.doi.org/10.1142/S0129054112400023 © World Scientific Publishing Company http://www.worldscientific.com/Transient algebra is a multi-valued algebra for hazard detection in gate circuits. Sequences of alternating 0's and 1's, called transients, represent signal values, and gates are modeled by extensions of boolean functions to transients. Formulas for computing the output transient of a gate from the input transients are known for NOT, AND, OR and XOR gates and their complements, but, in general, even the problem of deciding whether the length of the output transient exceeds a given bound is NP-complete. We propose a method of evaluating extensions of general boolean functions. We study a class of functions for which, instead of evaluating the extensions on a given set of transients, it is possible to get the same values by using transients derived from the given ones, but having length at most 3. We prove that all functions of three variables, as well as certain other functions, have this property, and can be efficiently evaluated.Natural Sciences and Engineering Research Council of Canada [OGP0000871]Department of Computer Science, University of Toront

Logic Circuits Timing Analysis Using Timed Logic Variables

Combinational logic circuit timing analysis is an important issue that all designers need to address. The present paper presents a simple and compact analysis procedure. We follow the guidelines drawn by previous methods, but we shall define new time-dependent logic variables that help us improve their efficiency. By using the methodology suggested, we shall replace a very laborious technique (pure delay circuit + time constants method) with a simpler procedure that can pinpoint the specific conditions for a logic circuit’s anomalous behaviour within a few simple steps. Considering the logic function implemented the methodology presented will require analysis of only a limited number of situations/combinations to determine the presence of an anomalous behaviour. When anomalous behaviour is identified, the methodology provides a clear timing description

On the Complexity of the Evaluation of Transient Extensions of Boolean Functions

Transient algebra is a multi-valued algebra for hazard detection in gate circuits. Sequences of alternating 0's and 1's, called transients, represent signal values, and gates are modeled by extensions of boolean functions to transients. Formulas for computing the output transient of a gate from the input transients are known for NOT, AND, OR} and XOR gates and their complements, but, in general, even the problem of deciding whether the length of the output transient exceeds a given bound is NP-complete. We propose a method of evaluating extensions of general boolean functions. We introduce and study a class of functions with the following property: Instead of evaluating an extension of a boolean function on a given set of transients, it is possible to get the same value by using transients derived from the given ones, but having length at most 3. We prove that all functions of three variables, as well as certain other functions, have this property, and can be efficiently evaluated