Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2105.03531

On the Complexity of Verification of Time-Sensitive Distributed Systems: Technical Report

Max Kanovich·Tajana Ban Kirigin·Vivek Nigam·Andre Scedrov·Carolyn Talcott
View original source ↗Read source document ↗Export metadata ↓

Abstract

This paper develops a Multiset Rewriting language with explicit time for the specification and analysis of Time-Sensitive Distributed Systems (TSDS). Goals are often specified using explicit time constraints. A good trace is an infinite trace in which the goals are satisfied perpetually despite possible interference from the environment. In our previous work (FORMATS 2016), we discussed two desirable properties of TSDSes, realizability (there exists a good trace) and survivability (where, in addition, all admissible traces are good). Here we consider two additional properties, recoverability (all compliant traces do not reach points-of-no-return) and reliability (the system can always continue functioning using a good trace). Following (FORMATS 2016), we focus on a class of systems called Progressing Timed Systems (PTS), where intuitively only a finite number of actions can be carried out in a bounded time period. We prove that for this class of systems the properties of recoverability and reliability coincide and are PSPACE-complete. Moreover, if we impose a bound on time (as in bounded model-checking), we show that for PTS the reliability property is in the $\Pi_2^p$ class of the polynomial hierarchy, a subclass of PSPACE. We also show that the bounded survivability is both NP-hard and coNP-hard.

Explore related subjects

cs.CCcs.LO

Keep this discovery

BibTeXRIS

Max Kanovich, Tajana Ban Kirigin, Vivek Nigam, Andre Scedrov, Carolyn Talcott. 2021-05-07. On the Complexity of Verification of Time-Sensitive Distributed Systems: Technical Report. https://arxiv.org/abs/2105.03531

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

The Computational Complexity of Holant Problems on 4-regular Graphs from the Stable Subgroup Sequence of $SL(2,\mathbb{C})$

The Holant framework provides a general setting for studying counting problems and includes graph homomorphisms (\#GH) and counting constraint satisfaction problems (\#CSP) as special cases. Over the past twenty years, a series of computational complexity dichotomies have been established for Holant problems, but the classification for complex-valued signatures is still open. The main obstacle is the case in which all signatures have even arity. In this paper, we establish a dichotomy for Holant problems with a complex-valued 4-ary signature, which is a key base case for the full classification of Holant problems. We present a new strategy by introducing Schur's theorem, the classification of finite subgroups of $\mathrm{SL}(2,\mathbb{C})$ and stable subgroup sequences into the proof. These new techniques are of independent interest.

cs.CC↗
arXiv2026

Topology inside NC$^1$

We show that ACC$^0$ is precisely what can be computed with constant-width circuits of polynomial size and polylogarithmic genus. This extends a characterization given by Hansen, showing that planar constant-width circuits also characterize ACC$^0$. Thus polylogarithmic genus provides no additional computational power in this model. We consider other generalizations of planarity, including crossing number and thickness. We show that constant-width circuits of polynomial size and thickness two already suffice to capture all of NC$^1$.

cs.CC↗