Risk Assessment for One-Counter Threads

Abstract

Threads as contained in a thread algebra are used for the modeling of sequential program behavior. A thread that may use a counter to control its execution is called a ‘one-counter thread’. In this paper the decidability of risk assessment (a certain form of action forecasting) for one-counter threads is proved. This relates to Cohen’s impossibility result on virus detection (Comput. Secur. 6(1), 22–35, 1984). Our decidability result follows from a general property of the traces of one-counter threads: if a state is reachable from some initial state, then it is also reachable along a path in which all counter values stay below a fixed bound that depends only on the initial and final counter value. A further consequence is that the reachability of a state is decidable. These properties are based on a result for ω-one counter machines by Rosier and Yen (SIAM J. Comput. 16(5), 779–807, 1987).