{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,2]],"date-time":"2026-07-02T16:08:18Z","timestamp":1783008498789,"version":"3.54.5"},"reference-count":23,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2025,4,11]],"date-time":"2025-04-11T00:00:00Z","timestamp":1744329600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European Union Next-GenerationEU - National Recovery and Resilience Plan (NRRP) \u2013 MISSION 4 COMPONENT 2, INVESTIMENT 1.3 \u2013 CUP","award":["H73C22000890001"],"award-info":[{"award-number":["H73C22000890001"]}]},{"name":"Research Project INDAM GNCS 2024 - CUP","award":["E53C23001670001"],"award-info":[{"award-number":["E53C23001670001"]}]},{"name":"\u201cNiRvAna - Noninterference and Reversibility Analysis in Private Blockchains\u201d","award":["PRIN 2020 - CUP N. 20202FCJMH"],"award-info":[{"award-number":["PRIN 2020 - CUP N. 20202FCJMH"]}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Model. Comput. Simul."],"published-print":{"date-parts":[[2025,4,30]]},"abstract":"<jats:p>\n            A blockchain is an immutable ledger driven by a distributed consensus protocol. In public blockchains, such as Bitcoin and Ethereum Classic, consensus is established through a computational effort called Proof-of-Work (PoW). Special users called\n            <jats:italic>miners<\/jats:italic>\n            contribute to the PoW in exchange for a fee and also verify the data stored in blocks mined by the other miners. Here is where the Verifier\u2019s Dilemma emerges. Verification of blocks does not receive a reward, and to maximise their profits, miners may be incentivised to forego verifying blocks and to only invest their resources in PoW. In this article, we study the Verifier\u2019s Dilemma and a possible countermeasure consisting of the injection of invalid blocks using a quantitative model based on Markovian process algebra. To avoid the state space explosion problem, we study the underlying Markov chain by using a lumping that allows us to derive closed-form solutions for interesting performance indices. The analysis demonstrates the circumstances under which non-verifying miners gain fees higher than those of verifying miners. The model also allows us to derive the optimal rate at which invalid blocks must be injected so that skipping the verifying phase becomes economically disadvantageous whereas the throughput of the blockchain is only minimally reduced. The impact on miners\u2019 rewards and overall performance is also assessed.\n          <\/jats:p>","DOI":"10.1145\/3723874","type":"journal-article","created":{"date-parts":[[2025,3,15]],"date-time":"2025-03-15T11:23:56Z","timestamp":1742037836000},"page":"1-24","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Verifier's Dilemma in Proof-of-Work Public Blockchains: A Quantitative Analysis"],"prefix":"10.1145","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5893-8259","authenticated-orcid":false,"given":"Daria","family":"Smuseva","sequence":"first","affiliation":[{"name":"Department of Environmental Sciences, Informatics and Statistics, Ca' Foscari University of Venice, Venezia, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5958-1204","authenticated-orcid":false,"given":"Andrea","family":"Marin","sequence":"additional","affiliation":[{"name":"Department of Environmental Sciences, Informatics and Statistics, Ca' Foscari University of Venice, Venezia, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1189-4439","authenticated-orcid":false,"given":"Sabina","family":"Rossi","sequence":"additional","affiliation":[{"name":"Department of Environmental Sciences, Informatics and Statistics, Ca' Foscari University of Venice, Venezia, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7233-6943","authenticated-orcid":false,"given":"Aad","family":"Van Moorsel","sequence":"additional","affiliation":[{"name":"School of Computer Science, University of Birmingham, Birmingham, United Kingdom of Great Britain and Northern Ireland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2025,4,11]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1109\/DSN48063.2020.00038"},{"key":"e_1_3_2_3_2","doi-asserted-by":"crossref","unstructured":"Maher Alharby and Aad van Moorsel. 2020. BlockSim: An extensible simulation tool for blockchain systems. Front. Blockchain 3 Art. 28 (2020) 1\u201316.","DOI":"10.3389\/fbloc.2020.00028"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ic.2018.04.002"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.1109\/EMPDP.2019.8671637"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.1145\/3427921.3450249"},{"key":"e_1_3_2_7_2","unstructured":"Vitalik Buterin. 2014. Ethereum: A next-generation smart contract and decentralized application platform. Ethereum White Paper. (2014)."},{"key":"e_1_3_2_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2019.02.001"},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","DOI":"10.1145\/3491053"},{"key":"e_1_3_2_10_2","article-title":"YODA: Enabling computationally intensive contracts on blockchains with Byzantine and Selfish nodes","author":"Das Sourav","year":"2018","unstructured":"Sourav Das, Vinay Joseph Ribeiro, and Abhijeet Anand. 2018. YODA: Enabling computationally intensive contracts on blockchains with Byzantine and Selfish nodes. arXiv preprint arXiv:1811.03265 (2018).","journal-title":"arXiv preprint arXiv:1811.03265"},{"key":"e_1_3_2_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00446-019-00357-z"},{"key":"e_1_3_2_12_2","unstructured":"Marko Dimja\u0161evi\u0107 and Nicholas Clarke. 2019. Specification of the Blockchain Layer. Retrieved from https:\/\/github.com\/input-output-hk\/cardano-ledger\/releases\/latest\/download\/byron-blockchain.pdf"},{"key":"e_1_3_2_13_2","first-page":"67","volume-title":"International Conference on Financial Cryptography and Data Security","author":"Pontiveros Beltr\u00e1n Borja Fiz","year":"2019","unstructured":"Beltr\u00e1n Borja Fiz Pontiveros, Christof Ferreira Torres, et\u00a0al. 2019. Sluggish mining: Profiting from the Verifier\u2019s Dilemma. In International Conference on Financial Cryptography and Data Security. Springer, 67\u201381."},{"key":"e_1_3_2_14_2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511569951"},{"key":"e_1_3_2_15_2","doi-asserted-by":"publisher","DOI":"10.4108\/icst.valuetools.2013.254408"},{"key":"e_1_3_2_16_2","first-page":"1353","volume-title":"27th USENIX Security Symposium (USENIX Security\u201918)","author":"Kalodner Harry","year":"2018","unstructured":"Harry Kalodner, Steven Goldfeder, Xiaoqi Chen, S. Matthew Weinberg, and Edward W. Felten. 2018. Arbitrum: Scalable, private smart contracts. In 27th USENIX Security Symposium (USENIX Security\u201918). 1353\u20131370."},{"key":"e_1_3_2_17_2","volume-title":"Finite Markov Chains","author":"Kemeny John G.","year":"1976","unstructured":"John G. Kemeny and J. Laurie Snell. 1976. Finite Markov Chains. 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A scalable verification solution for blockchains. arXiv preprint arXiv:1908.04756 (2019).","journal-title":"arXiv preprint arXiv:1908.04756"},{"key":"e_1_3_2_23_2","doi-asserted-by":"publisher","DOI":"10.1145\/1530873.1530880"},{"key":"e_1_3_2_24_2","doi-asserted-by":"publisher","DOI":"10.1109\/SOSE.2017.33"}],"container-title":["ACM Transactions on Modeling and Computer Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3723874","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3723874","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T01:19:00Z","timestamp":1750295940000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3723874"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,11]]},"references-count":23,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2025,4,30]]}},"alternative-id":["10.1145\/3723874"],"URL":"https:\/\/doi.org\/10.1145\/3723874","relation":{},"ISSN":["1049-3301","1558-1195"],"issn-type":[{"value":"1049-3301","type":"print"},{"value":"1558-1195","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,4,11]]},"assertion":[{"value":"2023-03-06","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-03-07","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-04-11","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}