Recursive Decomposition of Progress Graphs

Search of a state transition system is traditionally how deadlock detection for concurrent programs has been accomplished. This paper examines an approach to deadlock detection that uses geometric semantics involving the topo-logical notion of dihomotopy to partition the state space into components; after that the reduced state space is exhaustively searched. Prior work partitioned the state space inductively. in this paper we show that a recursive technique provides greater reduction of the size of the state transition system and therefore more efficient deadlock detection. If the preprocessing can be done efficiently, then for large problems we expect to see more efficient deadlock detection and eventually more efficient verification of some temporal properties. © 2009 IEEE

Deadlock detection and dihomotopic reduction via progress shell decomposition

Deadlock detection for concurrent programs has traditionally been accomplished by symbolic methods or by search of a state transition system. This work examines an approach that uses geometric semantics involving the topological notion of dihomotopy to partition the state space into components, followed by an exhaustive search of the reduced state space. Prior work partitioned the state-space inductively; however, this work shows that a technique motivated by recursion further reduces the size of the state transition system. The reduced state space results in asymptotic improvements in overall runtime for verification. Thus, with efficient partitioning, more efficient deadlock detection and eventually more efficient verification of some temporal properties can be expected for large problems --Abstract, page iii