Dominik Klumpp

Constantin Enea, Azadeh Farzan, Dominik Klumpp

The verification of reductions, representative subsets of interleavings, simplifies correctness proofs of parameterized concurrent programs. We introduce an expressive class of syntactic reductions, which we call natural reductions. Natural reductions are specified by introducing atomic blocks and global rendezvous points in the parameterized program's thread template. We study the problem of deciding whether a given natural reduction is sound wrt. a given (semi-)commutativity relation. In the case that there is no synchronization between threads, we present a sound and complete polynomial-time algorithm. In the case where synchronization is considered, we provide a general lower bound for the problem (parametric in the synchronization mechanism), and show that the problem is coNP-hard already for a simple mechanism like locking.

Dominik Klumpp, Jandson S. Ribeiro

Despite significant efforts towards extending the AGM paradigm of belief change beyond finitary logics, the computational aspects of AGM have remained almost untouched. We investigate the computability of AGM contraction on non-finitary logics, and show an intriguing negative result: there are infinitely many uncomputable AGM contraction functions in such logics. Drastically, we also show that the current de facto standard strategies to control computability, which rely on restricting the space of epistemic states, fail: uncomputability remains in all non-finitary cases. Motivated by this disruptive result, we propose new approaches to controlling computability beyond the finitary realm. Using Linear Temporal Logic (LTL) as a case study, we identify an infinite class of fully-rational AGM contraction functions that are computable by design. We use Büchi automata to construct such functions, and to represent and reason about LTL beliefs.