It is known that interprocedural detection of copy constants and elimination of faint code in parallel programs are undecidable problems, if base statements are assumed to execute atomically. We show that these problems become decidable, if this assumption is abandoned. So, the (unrealistic) idealization from program verification “atomic execution of base statements” introduced in order to simplify matters, actually increases the difficulty of these problems from the point of view of program analysis: amazingly these problems become more tractable if we adopt a less idealized, more realistic model of execution.
We introduce an effective abstract domain of antichains of dependence traces that allows us to perform a precise interprocedural dependence analysis in (non-atomically executing) parallel programs. The main idea is to trace sequences of dependences exhibited successively by program executions. We define operations on antichains of dependence traces and show that they precisely abstract the corresponding operations on sets of non-atomic program executions. Using these operations, we can analyze dependences by means of an abstract interpretation of constraint systems that characterize sets of program executions of interest. The result of the dependence analysis can in turn be used to detect all copy constants and to eliminate faint code.
While the run-time of the algorithms is exponential in the number of program variables, it is polynomial in the program size. Hence, they are polynomial-time algorithms if the number of program variables is bounded. In order to justify their overall exponential run-time, we show that both detection of copy constants and elimination of faint code are intractable (NP-hard) even when the atomic execution idealization is abandoned. This holds already for parallel programs without loops or procedures.
