arXiv subjects

Aayush Rajasekaran

Publications and source records attributed to Aayush Rajasekaran.

5 recordsLinked to original sources

arXiv2025

OPTIMUMP2P: Fast and Reliable Gossiping in P2P Networks

Gossip algorithms are pivotal in the dissemination of information within decentralized systems. Consequently, numerous gossip libraries have been developed and widely utilized especially in blockchain protocols for the propagation of blocks and transactions. A well-established library is libp2p, which provides two gossip algorithms: floodsub and gossipsub. These algorithms enable the delivery of published messages to a set of peers. In this work we aim to enhance the performance and reliability of libp2p by introducing OPTIMUMP2P, a novel gossip algorithm that leverages the capabilities of Random Linear Network Coding (RLNC) to expedite the dissemination of information in a peer-to-peer (P2P) network while ensuring reliable delivery, even in the presence of malicious actors capable of corrupting the transmitted data. Preliminary research from the Ethereum Foundation has demonstrated the use of RLNC in the significant improvement in the block propagation time [14]. Here we present extensive evaluation results both in simulation and real-world environments that demonstrate the performance gains of OPTIMUMP2P over the Gossipsub protocol.

cs.DC↗

arXiv2019

An Interleaving Hybrid Consensus Protocol

We introduce Unity Interleave, a new consensus algorithm for public blockchain settings. It is an eventual consistency protocol merging the Proof-of-Work (PoW) and Proof-of-Stake (PoS) into a coherent stochastic process. It builds upon research previously done for the Unity protocol, improving security while maintaining fairness and scalability.

cs.CR↗

arXiv2018

Lagrange's Theorem for Binary Squares

We show how to prove theorems in additive number theory using a decision procedure based on finite automata. Among other things, we obtain the following analogue of Lagrange's theorem: every natural number > 686 is the sum of at most 4 natural numbers whose canonical base-2 representation is a binary square, that is, a string of the form xx for some block of bits x. Here the number 4 is optimal. While we cannot embed this theorem itself in a decidable theory, we show that stronger lemmas that imply that the theorem can be embedded in decidable theories, and show how automated methods can be used to search for these stronger lemmas.

math.NT↗

arXiv2017

Sums of Palindromes: an Approach via Automata

Recently, Cilleruelo, Luca, & Baxter proved, for all bases b >= 5, that every natural number is the sum of at most 3 natural numbers whose base-b representation is a palindrome. However, the cases b = 2, 3, 4 were left unresolved. We prove, using a decision procedure based on automata, that every natural number is the sum of at most 4 natural numbers whose base-2 representation is a palindrome. Here the constant 4 is optimal. We obtain similar results for bases 3 and 4, thus completely resolving the problem. We consider some other variations on this problem, and prove similar results. We argue that heavily case-based proofs are a good signal that a decision procedure may help to automate the proof.

cs.FL↗

arXiv2016

On the State Complexity of the Shuffle of Regular Languages

We investigate the shuffle operation on regular languages represented by complete deterministic finite automata. We prove that $f(m,n)=2^{mn-1} + 2^{(m-1)(n-1)}(2^{m-1}-1)(2^{n-1}-1)$ is an upper bound on the state complexity of the shuffle of two regular languages having state complexities $m$ and $n$, respectively. We also state partial results about the tightness of this bound. We show that there exist witness languages meeting the bound if $2\le m\le 5$ and $n\ge2$, and also if $m=n=6$. Moreover, we prove that in the subset automaton of the NFA accepting the shuffle, all $2^{mn}$ states can be distinguishable, and an alphabet of size three suffices for that. It follows that the bound can be met if all $f(m,n)$ states are reachable. We know that an alphabet of size at least $mn$ is required provided that $m,n \ge 2$. The question of reachability, and hence also of the tightness of the bound $f(m,n)$ in general, remains open.

cs.FL↗