Reachability in Binary Multithreaded Programs Is Polynomial
Alexander Malkis, Steffen Borgwardt · 2017
Automatic finding of bugs in multithreaded programs is an important but inherently difficult task, even in the finite-state interleaving-semantics case. The complexity of this task has only been partially explored so far. We measure quantities such as the diameter, which is the longest finite distance realizable in the transition graph of the program, the local diameter, which is the maximum distance from any program state to any thread-local state, and the computational complexity of bugfinding. For the subclass of so-called binary multithreaded programs, we prove new bounds: all these quantities are majorized by a polynomial and, in certain cases, by a linear, logarithmic, or even constant function. Our bounds present a preparation step towards the corresponding polynomial-bound claims for general programs. These claims contrast sharply with the common belief that the main obstacle to analyzing concurrent programs is the exponential state explosion in the number of threads.