Context (archaeology)

Algorithm

Engineering

Pure mathematics

Biology

Theoretical computer science

Field (mathematics)

Set (abstract data type)

Computer science

Decidability

Reachability

Paleontology

Mathematics

Flow (mathematics)

Electronic engineering

Path (computing)

Geometry

Sensitivity (control systems)

Programming language

Undecidable problem

Proceedings of the ACM on Programming Languages

Precise static analyses are context-, field- and flow-sensitive. Context- and field-sensitivity are both expressible as context-free language (CFL) reachability problems. Solving both CFL problems along the same data-flow path is undecidable, which is why most flow-sensitive data-flow analyses over-approximate field-sensitivity through k -limited access-path, or through access graphs. Unfortunately, as our experience and this paper show, both representations do not scale very well when used to analyze programs with recursive data structures. Any single CFL-reachability problem is efficiently solvable, by means of a pushdown system. This work thus introduces the concept of synchronized pushdown systems (SPDS). SPDS encode both procedure calls/returns and field stores/loads as separate but “synchronized” CFL reachability problems. An SPDS solves both individual problems precisely, and approximation occurs only in corner cases that are apparently rare in practice: at statements where both problems are satisfied but not along the same data-flow path. SPDS are also efficient: formal complexity analysis shows that SPDS shift the complexity from | F | 3 k under k -limiting to | S || F | 2 , where F is the set of fields and S the set of statements involved in a data-flow. Our evaluation using DaCapo shows this shift to pay off in practice: SPDS are almost as efficient as k -limiting with k =1 although their precision equals k =∞. For a typestate analysis SPDS accelerate the analysis up to 83× for data-flows of objects that involve many field accesses but span rather few methods. We conclude that SPDS can provide high precision and further improve scalability, in particularly when used in analyses that expose rather local data flows.

Context-, flow-, and field-sensitive data-flow analysis using synchronized Pushdown systems