arXiv subjects

A. R. Balasubramanian

Publications and source records attributed to A. R. Balasubramanian.

23 records · Page 2Linked to original sources

arXiv2020

Complexity of controlled bad sequences over finite sets of $\mathbb{N}^d$

We provide upper and lower bounds for the length of controlled bad sequences over the majoring and the minoring orderings of finite sets of $\mathbb{N}^d$. The results are obtained by bounding the length of such sequences by functions from the Cichon hierarchy. This allows us to translate these results to bounds over the fast-growing complexity classes. The obtained bounds are proven to be tight for the majoring ordering, which solves a problem left open by Abriola, Figueira and Senno (Theor. Comp. Sci, Vol. 603). Finally, we use the results on controlled bad sequences to prove upper bounds for the emptiness problem of some classes of automata.

cs.LO↗

arXiv2020

Characterizing consensus in the Heard-Of model

The Heard-Of model is a simple and relatively expressive model of distributed computation. Because of this, it has gained a considerable attention of the verification community. We give a characterization of all algorithms solving consensus in a fragment of this model. The fragment is big enough to cover many prominent consensus algorithms. The characterization is purely syntactic: it is expressed in terms of some conditions on the text of the algorithm. One of the recent methods of verification of distributed algorithms is to abstract an algorithm to the Heard-Of model and then to verify the abstract algorithm using semi-automatic procedures. Our results allow, in some cases, to avoid the second step in this methodology.

cs.LO↗

arXiv2019

Generalized threshold arrangements

An arrangement of hyperplanes is a finite collection of hyperplanes in a real Euclidean space. To such a collection one associates the characteristic polynomial that encodes the combinatorics of intersections of the hyperplanes. Finding the characteristic polynomial of the Shi threshold and the Catalan threshold arrangements was an open problem in Stanley's list of problems in [1]. Seunghyun Seo solved both the problems by clever arguments using the finite field method in [3,4]. However, in his paper, he left open the problem of computing the characteristic polynomial of a broader class of threshold arrangements, the so-called "generalized threshold" arrangements whose defining set of hyperplanes is given by $x_i + x_j = -l,-l+1,...,m-1,m$ for $1 \le i < j \le n$ where $l,m \in \mathbb{N}$. In this paper, we present a method for computing the characteristic polynomial of this family of arrangements.

math.CO↗

arXiv2018

Parameterized Verification of Coverability in Well-Structured Broadcast Networks

Parameterized verification of coverability in broadcast networks with finite state processes has been studied for different types of models and topologies. In this paper, we attempt to develop a theory of broadcast networks in which the processes can be well-structured transition systems. The resulting formalism is called well-structured broadcast networks. We give an algorithm to decide coverability of well-structured broadcast networks when reconfiguration of links between nodes is allowed. Further, for various types of communication topologies, we also prove the decidability of coverability in the static case as well. We do this by showing that for these types of static communication topologies, the broadcast network itself is a well-structured transition system, hence proving the decidability of coverability in the broadcast network.

cs.LO↗

arXiv2018

Parameterized verification of synchronization in constrained reconfigurable broadcast networks

Reconfigurable broadcast networks provide a convenient formalism for modelling and reasoning about networks of mobile agents broadcasting messages to other agents following some (evolving) communication topology. The parameterized verification of such models aims at checking whether a given property holds irrespective of the initial configuration (number of agents, initial states and initial communication topology). We focus here on the synchronization property, asking whether all agents converge to a set of target states after some execution. This problem is known to be decidable in polynomial time when no constraints are imposed on the evolution of the communication topology (while it is undecidable for static broadcast networks). In this paper we investigate how various constraints on reconfigurations affect the decidability and complexity of the synchronization problem. In particular, we show that when bounding the number of reconfigured links between two communications steps by a constant, synchronization becomes undecidable; on the other hand, synchronization remains decidable in PTIME when the bound grows with the number of agents.

cs.LO↗