3 Search Results for "Rajasekaran, Aayush"

Document
DOI: 10.4230/LIPIcs.AFT.2025.16
Nakamoto Consensus from Multiple Resources

Authors: Mirza Ahad Baig, Christoph U. Günther, and Krzysztof Pietrzak

Published in: LIPIcs, Volume 354, 7th Conference on Advances in Financial Technologies (AFT 2025)

Abstract
The blocks in the Bitcoin blockchain "record" the amount of work W that went into creating them through proofs of work. When honest parties control a majority of the work, consensus is achieved by picking the chain with the highest recorded weight. Resources other than work have been considered to secure such longest-chain blockchains. In Chia, blocks record the amount of disk-space S (via a proof of space) and sequential computational steps V (through a VDF). In this paper, we ask what weight functions Γ(S,V,W) (that assign a weight to a block as a function of the recorded space, speed, and work) are secure in the sense that whenever the weight of the resources controlled by honest parties is larger than the weight of adversarial parties, the blockchain is secure against private double-spending attacks. We completely classify such functions in an idealized "continuous" model: Γ(S,V,W) is secure against private double-spending attacks if and only if it is homogeneous of degree one in the "timed" resources V and W, i.e., αΓ(S,V,W) = Γ(S,α V, α W). This includes the Bitcoin rule Γ(S,V,W) = W and the Chia rule Γ(S,V,W) = S ⋅ V. In a more realistic model where blocks are created at discrete time-points, one additionally needs some mild assumptions on the dependency on S (basically, the weight should not grow too much if S is slightly increased, say linear as in Chia). Our classification is more general and allows various instantiations of the same resource. It provides a powerful tool for designing new longest-chain blockchains. E.g., consider combining different PoWs to counter centralization, say the Bitcoin PoW W₁ and a memory-hard PoW W₂. Previous work suggested to use W₁+W₂ as weight. Our results show that using e.g., √{W₁}⋅ √{W₂} or min{W₁,W₂} are also secure, and we argue that in practice these are much better choices.
Cite as

Mirza Ahad Baig, Christoph U. Günther, and Krzysztof Pietrzak. Nakamoto Consensus from Multiple Resources. In 7th Conference on Advances in Financial Technologies (AFT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 354, pp. 16:1-16:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{baig_et_al:LIPIcs.AFT.2025.16,
  author =	{Baig, Mirza Ahad and G\"{u}nther, Christoph U. and Pietrzak, Krzysztof},
  title =	{{Nakamoto Consensus from Multiple Resources}},
  booktitle =	{7th Conference on Advances in Financial Technologies (AFT 2025)},
  pages =	{16:1--16:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-400-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{354},
  editor =	{Avarikioti, Zeta and Christin, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AFT.2025.16},
  URN =		{urn:nbn:de:0030-drops-247353},
  doi =		{10.4230/LIPIcs.AFT.2025.16},
  annote =	{Keywords: Nakamoto Consensus, Heaviest-chain Rule, Resource Theory}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2018.18
Lagrange's Theorem for Binary Squares

Authors: P. Madhusudan, Dirk Nowotka, Aayush Rajasekaran, and Jeffrey Shallit

Published in: LIPIcs, Volume 117, 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)

Abstract
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 the theorem can be embedded in decidable theories, and show how automated methods can be used to search for these stronger lemmas.
Cite as

P. Madhusudan, Dirk Nowotka, Aayush Rajasekaran, and Jeffrey Shallit. Lagrange's Theorem for Binary Squares. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 18:1-18:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{madhusudan_et_al:LIPIcs.MFCS.2018.18,
  author =	{Madhusudan, P. and Nowotka, Dirk and Rajasekaran, Aayush and Shallit, Jeffrey},
  title =	{{Lagrange's Theorem for Binary Squares}},
  booktitle =	{43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
  pages =	{18:1--18:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-086-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{117},
  editor =	{Potapov, Igor and Spirakis, Paul and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.18},
  URN =		{urn:nbn:de:0030-drops-96003},
  doi =		{10.4230/LIPIcs.MFCS.2018.18},
  annote =	{Keywords: binary square, theorem-proving, finite automaton, decision procedure, decidable theory, additive number theory}
}
Document
DOI: 10.4230/LIPIcs.STACS.2018.54
Sums of Palindromes: an Approach via Automata

Authors: Aayush Rajasekaran, Jeffrey Shallit, and Tim Smith

Published in: LIPIcs, Volume 96, 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)

Abstract
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.
Cite as

Aayush Rajasekaran, Jeffrey Shallit, and Tim Smith. Sums of Palindromes: an Approach via Automata. In 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 96, pp. 54:1-54:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

Copy BibTex To Clipboard

@InProceedings{rajasekaran_et_al:LIPIcs.STACS.2018.54,
  author =	{Rajasekaran, Aayush and Shallit, Jeffrey and Smith, Tim},
  title =	{{Sums of Palindromes: an Approach via Automata}},
  booktitle =	{35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)},
  pages =	{54:1--54:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-062-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{96},
  editor =	{Niedermeier, Rolf and Vall\'{e}e, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2018.54},
  URN =		{urn:nbn:de:0030-drops-84976},
  doi =		{10.4230/LIPIcs.STACS.2018.54},
  annote =	{Keywords: finite automaton, nested-word automaton, decision procedure, palindrome, additive number theory}
}
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