Many program analyses need to reason about pairs of matching actions, such as call/return, lock/unlock, or set-field/get-field. The family Dyck languages { D k }, where has kinds parenthesis pairs, can be used model actions balanced parentheses. Consequently, many program-analysis problems formulated Dyck-reachability on edge-labeled digraphs. Interleaved (InterDyck-reachability), denoted by ⊙ ...

Many program-analysis problems can be formulated as graph-reachability problems. Interleaved Dyck language reachability ( InterDyck -reachability) is a fundamental framework to express wide variety of over edge-labeled graphs. The represents an intersection multiple matched-parenthesis languages (i.e., languages). In practice, program analyses typically leverage one achieve context-sensitivity,...

Chip-firing and rotor-routing are two well-studied examples of abelian networks. We study the complexity their respective reachability problems. show that problem is decidable in polynomial time, we give a simple characterization when chip-and-rotor configuration reachable from another one. For chip-firing, it has been known P if have class graphs whose period length (for example, Eulerian digr...

Many problems in interprocedural program analysis can be modeled as the context-free language (CFL) reachability problem on graphs and solved cubic time. Despite years of efforts, there are no known truly sub-cubic algorithms for this problem. We study related certification task: given an instance CFL reachability, small efficiently checkable certificates existence non-existence a path? show th...