Automatic detection of task-level parallelism (also referred to as functional, DAG, unstructured, or thread parallelism) at various levels of program granularity is becoming increasingly important for parallelizing and back-end compilers. Parallelizing compilers detect iteration-level or coarser granularity parallelism which is suitable for parallel computers; detection of parallelism at the statement-or operation-level is essential for most modern microprocessors, including superscalar and VLIW architectures. In this article we study the problem of detecting, expressing, and optimizing task-level parallelism, where “task” refers to a program statement of arbitrary granularity. Optimizing the amount of functional parallelism (by allowing synchronization between arbitrary nodes) in sequential programs requires the notion of precedence in terms of paths in graphs which incorporate control and data dependences. Precedences have been defined before in a different context; however, the definition was dependent on the ideas of parallel execution and time. We show that the problem of determining precedences statically is NP-complete. Determining precedence relationships is useful in finding the essential data dependences. We show that there exists a unique minimum set of essential data dependences; finding this minimum set is NP-hard and NP-easy. We also propose a heuristic algorithm for finding the set of essential data dependences. Static analysis of a program in the Perfect Benchmarks was done, and we present some experimental results.