Four-Valued Reasoning and Cyclic Circuits

Abstract

Allowing cycles in a logic circuit can be advantageous, for example, by reducing the number of gates required to implement a given Boolean function, or a set of functions. However, a cyclic circuit may easily be ill behaved. For instance, it may have some output wire oscillation instead of reaching a steady state. Propositional three-valued logic has long been used in tests for good behavior of cyclic circuits; a symbolic evaluation method known as ternary analysis provides one criterion for good behavior under certain assumptions about wire and gate delay. We revisit ternary analysis and argue for the use of four truth values. The fourth truth value allows for the distinction of undefined a..