Abstract
We study the fine-grained complexity of Leader Contributor Reachability (\(\mathsf {LCR}\)) and Bounded-Stage Reachability (\({\mathsf {BSR}}\)), two variants of the safety verification problem for shared-memory concurrent programs. For both problems, the memory is a single variable over a finite data domain. We contribute new verification algorithms and lower bounds based on the Exponential Time Hypothesis (\({\mathsf {ETH}}\)) and kernels.
Highlights
We study the fine-grained complexity of two safety verification problems [1,16, 27] for shared-memory concurrent programs
The motivation to reconsider these problems are recent developments in fine-grained complexity theory [6,10,30,33]. They suggest that classifications such as NP or even fixed-parameter tractability (FPT) are too coarse to explain the success of verification methods
We show how to modify the algorithm to solve instances of Leader Contributor Reachability (LCR) as they are likely to occur in practice
Summary
We study the fine-grained complexity of two safety verification problems [1,16, 27] for shared-memory concurrent programs. The motivation to reconsider these problems are recent developments in fine-grained complexity theory [6,10,30,33] They suggest that classifications such as NP or even FPT are too coarse to explain the success of verification methods. We give new verification algorithms for the two problems that, for the first time, can be proven optimal in the sense of finegrained complexity theory. -called fixed-parameter tractability (FPT) [11,13] proposes to identify parameters k so that the runtime is f (k)poly(n), where f is a computable function These parameters are powerful in the sense that they dominate the complexity. Fine-grained complexity is the study of upper and lower bounds on function f. We contribute fine-grained complexity results for verification problems on concurrent programs. We suggest kernel lower bounds as hardness indicators for verification problems. The finding is that FPT solutions are unlikely to exist
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
