From algebraic semantics to denotational semantics for Verilog

This paper considers how the algebraic semantics for Verilog relates with its denotational semantics. Our approach is to derive the denotational semantics from the algebraic semantics. We first present the algebraic laws for Verilog. Every program can be expressed as a guarded choice that can model the execution of a program. In order to investigate the parallel expansion laws, a sequence is introduced, which indicates the instantaneous action is due to which exact parallel component. A normal form is defined for each program by using the locality sequence. We provide a strategy for deriving the denotational semantics based on the algebraic normal form. Using the strategy, the denotational semantics for every program can be calculated. Program equivalence can also be explored by using the derived denotational semantics.