--- _id: '6378' abstract: - lang: eng text: 'In today''s cryptocurrencies, Hashcash proof of work is the most commonly-adopted approach to mining. In Hashcash, when a miner decides to add a block to the chain, she has to solve the difficult computational puzzle of inverting a hash function. While Hashcash has been successfully adopted in both Bitcoin and Ethereum, it has attracted significant and harsh criticism due to its massive waste of electricity, its carbon footprint and environmental effects, and the inherent lack of usefulness in inverting a hash function. Various other mining protocols have been suggested, including proof of stake, in which a miner''s chance of adding the next block is proportional to her current balance. However, such protocols lead to a higher entry cost for new miners who might not still have any stake in the cryptocurrency, and can in the worst case lead to an oligopoly, where the rich have complete control over mining. In this paper, we propose Hybrid Mining: a new mining protocol that combines solving real-world useful problems with Hashcash. Our protocol allows new miners to join the network by taking part in Hashcash mining without having to own an initial stake. It also allows nodes of the network to submit hard computational problems whose solutions are of interest in the real world, e.g.~protein folding problems. Then, miners can choose to compete in solving these problems, in lieu of Hashcash, for adding a new block. Hence, Hybrid Mining incentivizes miners to solve useful problems, such as hard computational problems arising in biology, in a distributed manner. It also gives researchers in other areas an easy-to-use tool to outsource their hard computations to the blockchain network, which has enormous computational power, by paying a reward to the miner who solves the problem for them. Moreover, our protocol provides strong security guarantees and is at least as resilient to double spending as Bitcoin.' article_processing_charge: No author: - first_name: Krishnendu full_name: Chatterjee, Krishnendu id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87 last_name: Chatterjee orcid: 0000-0002-4561-241X - first_name: Amir Kafshdar full_name: Goharshady, Amir Kafshdar id: 391365CE-F248-11E8-B48F-1D18A9856A87 last_name: Goharshady orcid: 0000-0003-1702-6584 - first_name: Arash full_name: Pourdamghani, Arash last_name: Pourdamghani citation: ama: 'Chatterjee K, Goharshady AK, Pourdamghani A. Hybrid Mining: Exploiting blockchain’s computational power for distributed problem solving. In: Proceedings of the 34th ACM Symposium on Applied Computing. Vol Part F147772. ACM; 2019:374-381. doi:10.1145/3297280.3297319' apa: 'Chatterjee, K., Goharshady, A. K., & Pourdamghani, A. (2019). Hybrid Mining: Exploiting blockchain’s computational power for distributed problem solving. In Proceedings of the 34th ACM Symposium on Applied Computing (Vol. Part F147772, pp. 374–381). Limassol, Cyprus: ACM. https://doi.org/10.1145/3297280.3297319' chicago: 'Chatterjee, Krishnendu, Amir Kafshdar Goharshady, and Arash Pourdamghani. “Hybrid Mining: Exploiting Blockchain’s Computational Power for Distributed Problem Solving.” In Proceedings of the 34th ACM Symposium on Applied Computing, Part F147772:374–81. ACM, 2019. https://doi.org/10.1145/3297280.3297319.' ieee: 'K. Chatterjee, A. K. Goharshady, and A. Pourdamghani, “Hybrid Mining: Exploiting blockchain’s computational power for distributed problem solving,” in Proceedings of the 34th ACM Symposium on Applied Computing, Limassol, Cyprus, 2019, vol. Part F147772, pp. 374–381.' ista: 'Chatterjee K, Goharshady AK, Pourdamghani A. 2019. Hybrid Mining: Exploiting blockchain’s computational power for distributed problem solving. Proceedings of the 34th ACM Symposium on Applied Computing. ACM Symposium on Applied Computing vol. Part F147772, 374–381.' mla: 'Chatterjee, Krishnendu, et al. “Hybrid Mining: Exploiting Blockchain’s Computational Power for Distributed Problem Solving.” Proceedings of the 34th ACM Symposium on Applied Computing, vol. Part F147772, ACM, 2019, pp. 374–81, doi:10.1145/3297280.3297319.' short: K. Chatterjee, A.K. Goharshady, A. Pourdamghani, in:, Proceedings of the 34th ACM Symposium on Applied Computing, ACM, 2019, pp. 374–381. conference: end_date: 2019-04-12 location: Limassol, Cyprus name: ACM Symposium on Applied Computing start_date: 2019-04-08 date_created: 2019-05-06T12:11:36Z date_published: 2019-04-01T00:00:00Z date_updated: 2024-03-27T23:30:33Z day: '01' ddc: - '004' department: - _id: KrCh doi: 10.1145/3297280.3297319 ec_funded: 1 external_id: isi: - '000474685800049' file: - access_level: open_access checksum: fbfbcd5a0c7a743862bfc3045539a614 content_type: application/pdf creator: dernst date_created: 2019-05-06T12:09:27Z date_updated: 2020-07-14T12:47:29Z file_id: '6379' file_name: 2019_ACM_Chatterjee.pdf file_size: 1023934 relation: main_file file_date_updated: 2020-07-14T12:47:29Z has_accepted_license: '1' isi: 1 language: - iso: eng month: '04' oa: 1 oa_version: Submitted Version page: 374-381 project: - _id: 2581B60A-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '279307' name: 'Quantitative Graph Games: Theory and Applications' - _id: 25892FC0-B435-11E9-9278-68D0E5697425 grant_number: ICT15-003 name: Efficient Algorithms for Computer Aided Verification - _id: 25832EC2-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: S 11407_N23 name: Rigorous Systems Engineering publication: Proceedings of the 34th ACM Symposium on Applied Computing publication_identifier: isbn: - '9781450359337' publication_status: published publisher: ACM pubrep_id: '1069' quality_controlled: '1' related_material: record: - id: '8934' relation: dissertation_contains status: public scopus_import: '1' status: public title: 'Hybrid Mining: Exploiting blockchain’s computational power for distributed problem solving' type: conference user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: Part F147772 year: '2019' ... --- _id: '6175' abstract: - lang: eng text: "We consider the problem of expected cost analysis over nondeterministic probabilistic programs,\r\nwhich aims at automated methods for analyzing the resource-usage of such programs.\r\nPrevious approaches for this problem could only handle nonnegative bounded costs.\r\nHowever, in many scenarios, such as queuing networks or analysis of cryptocurrency protocols,\r\nboth positive and negative costs are necessary and the costs are unbounded as well.\r\n\r\nIn this work, we present a sound and efficient approach to obtain polynomial bounds on the\r\nexpected accumulated cost of nondeterministic probabilistic programs.\r\nOur approach can handle (a) general positive and negative costs with bounded updates in\r\nvariables; and (b) nonnegative costs with general updates to variables.\r\nWe show that several natural examples which could not be\r\nhandled by previous approaches are captured in our framework.\r\n\r\nMoreover, our approach leads to an efficient polynomial-time algorithm, while no\r\nprevious approach for cost analysis of probabilistic programs could guarantee polynomial runtime.\r\nFinally, we show the effectiveness of our approach using experimental results on a variety of programs for which we efficiently synthesize tight resource-usage bounds." article_processing_charge: No author: - first_name: Peixin full_name: Wang, Peixin last_name: Wang - first_name: Hongfei full_name: Fu, Hongfei id: 3AAD03D6-F248-11E8-B48F-1D18A9856A87 last_name: Fu - first_name: Amir Kafshdar full_name: Goharshady, Amir Kafshdar id: 391365CE-F248-11E8-B48F-1D18A9856A87 last_name: Goharshady orcid: 0000-0003-1702-6584 - first_name: Krishnendu full_name: Chatterjee, Krishnendu id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87 last_name: Chatterjee orcid: 0000-0002-4561-241X - first_name: Xudong full_name: Qin, Xudong last_name: Qin - first_name: Wenjun full_name: Shi, Wenjun last_name: Shi citation: ama: 'Wang P, Fu H, Goharshady AK, Chatterjee K, Qin X, Shi W. Cost analysis of nondeterministic probabilistic programs. In: PLDI 2019: Proceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation. Association for Computing Machinery; 2019:204-220. doi:10.1145/3314221.3314581' apa: 'Wang, P., Fu, H., Goharshady, A. K., Chatterjee, K., Qin, X., & Shi, W. (2019). Cost analysis of nondeterministic probabilistic programs. In PLDI 2019: Proceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation (pp. 204–220). Phoenix, AZ, United States: Association for Computing Machinery. https://doi.org/10.1145/3314221.3314581' chicago: 'Wang, Peixin, Hongfei Fu, Amir Kafshdar Goharshady, Krishnendu Chatterjee, Xudong Qin, and Wenjun Shi. “Cost Analysis of Nondeterministic Probabilistic Programs.” In PLDI 2019: Proceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation, 204–20. Association for Computing Machinery, 2019. https://doi.org/10.1145/3314221.3314581.' ieee: 'P. Wang, H. Fu, A. K. Goharshady, K. Chatterjee, X. Qin, and W. Shi, “Cost analysis of nondeterministic probabilistic programs,” in PLDI 2019: Proceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation, Phoenix, AZ, United States, 2019, pp. 204–220.' ista: 'Wang P, Fu H, Goharshady AK, Chatterjee K, Qin X, Shi W. 2019. Cost analysis of nondeterministic probabilistic programs. PLDI 2019: Proceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation. PLDI: Conference on Programming Language Design and Implementation, 204–220.' mla: 'Wang, Peixin, et al. “Cost Analysis of Nondeterministic Probabilistic Programs.” PLDI 2019: Proceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation, Association for Computing Machinery, 2019, pp. 204–20, doi:10.1145/3314221.3314581.' short: 'P. Wang, H. Fu, A.K. Goharshady, K. Chatterjee, X. Qin, W. Shi, in:, PLDI 2019: Proceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation, Association for Computing Machinery, 2019, pp. 204–220.' conference: end_date: 2019-06-26 location: Phoenix, AZ, United States name: 'PLDI: Conference on Programming Language Design and Implementation' start_date: 2019-06-22 date_created: 2019-03-25T10:13:25Z date_published: 2019-06-08T00:00:00Z date_updated: 2024-03-27T23:30:33Z day: '08' ddc: - '000' department: - _id: KrCh doi: 10.1145/3314221.3314581 ec_funded: 1 external_id: arxiv: - '1902.04659' isi: - '000523190300014' file: - access_level: open_access checksum: 703a5e9b8c8587f2a44085ffd9a4db64 content_type: application/pdf creator: akafshda date_created: 2019-03-25T10:11:22Z date_updated: 2020-07-14T12:47:20Z file_id: '6176' file_name: paper.pdf file_size: 4051066 relation: main_file file_date_updated: 2020-07-14T12:47:20Z has_accepted_license: '1' isi: 1 keyword: - Program Cost Analysis - Program Termination - Probabilistic Programs - Martingales language: - iso: eng month: '06' oa: 1 oa_version: Submitted Version page: 204-220 project: - _id: 25892FC0-B435-11E9-9278-68D0E5697425 grant_number: ICT15-003 name: Efficient Algorithms for Computer Aided Verification - _id: 25863FF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: S11407 name: Game Theory - _id: 25832EC2-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: S 11407_N23 name: Rigorous Systems Engineering - _id: 2581B60A-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '279307' name: 'Quantitative Graph Games: Theory and Applications' - _id: 266EEEC0-B435-11E9-9278-68D0E5697425 name: Quantitative Game-theoretic Analysis of Blockchain Applications and Smart Contracts publication: 'PLDI 2019: Proceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation' publication_status: published publisher: Association for Computing Machinery quality_controlled: '1' related_material: record: - id: '5457' relation: earlier_version status: public - id: '8934' relation: dissertation_contains status: public scopus_import: '1' status: public title: Cost analysis of nondeterministic probabilistic programs type: conference user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 year: '2019' ... --- _id: '6490' abstract: - lang: eng text: "Smart contracts are programs that are stored and executed on the Blockchain and can receive, manage and transfer money (cryptocurrency units). Two important problems regarding smart contracts are formal analysis and compiler optimization. Formal analysis is extremely important, because smart contracts hold funds worth billions of dollars and their code is immutable after deployment. Hence, an undetected bug can cause significant financial losses. Compiler optimization is also crucial, because every action of a smart contract has to be executed by every node in the Blockchain network. Therefore, optimizations in compiling smart contracts can lead to significant savings in computation, time and energy.\r\n\r\nTwo classical approaches in program analysis and compiler optimization are intraprocedural and interprocedural analysis. In intraprocedural analysis, each function is analyzed separately, while interprocedural analysis considers the entire program. In both cases, the analyses are usually reduced to graph problems over the control flow graph (CFG) of the program. These graph problems are often computationally expensive. Hence, there has been ample research on exploiting structural properties of CFGs for efficient algorithms. One such well-studied property is the treewidth, which is a measure of tree-likeness of graphs. It is known that intraprocedural CFGs of structured programs have treewidth at most 6, whereas the interprocedural treewidth cannot be bounded. This result has been used as a basis for many efficient intraprocedural analyses.\r\n\r\nIn this paper, we explore the idea of exploiting the treewidth of smart contracts for formal analysis and compiler optimization. First, similar to classical programs, we show that the intraprocedural treewidth of structured Solidity and Vyper smart contracts is at most 9. Second, for global analysis, we prove that the interprocedural treewidth of structured smart contracts is bounded by 10 and, in sharp contrast with classical programs, treewidth-based algorithms can be easily applied for interprocedural analysis. Finally, we supplement our theoretical results with experiments using a tool we implemented for computing treewidth of smart contracts and show that the treewidth is much lower in practice. We use 36,764 real-world Ethereum smart contracts as benchmarks and find that they have an average treewidth of at most 3.35 for the intraprocedural case and 3.65 for the interprocedural case.\r\n" article_processing_charge: No author: - first_name: Krishnendu full_name: Chatterjee, Krishnendu id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87 last_name: Chatterjee orcid: 0000-0002-4561-241X - first_name: Amir Kafshdar full_name: Goharshady, Amir Kafshdar id: 391365CE-F248-11E8-B48F-1D18A9856A87 last_name: Goharshady orcid: 0000-0003-1702-6584 - first_name: Ehsan Kafshdar full_name: Goharshady, Ehsan Kafshdar last_name: Goharshady citation: ama: 'Chatterjee K, Goharshady AK, Goharshady EK. The treewidth of smart contracts. In: Proceedings of the 34th ACM Symposium on Applied Computing. Vol Part F147772. ACM; :400-408. doi:10.1145/3297280.3297322' apa: 'Chatterjee, K., Goharshady, A. K., & Goharshady, E. K. (n.d.). The treewidth of smart contracts. In Proceedings of the 34th ACM Symposium on Applied Computing (Vol. Part F147772, pp. 400–408). Limassol, Cyprus: ACM. https://doi.org/10.1145/3297280.3297322' chicago: Chatterjee, Krishnendu, Amir Kafshdar Goharshady, and Ehsan Kafshdar Goharshady. “The Treewidth of Smart Contracts.” In Proceedings of the 34th ACM Symposium on Applied Computing, Part F147772:400–408. ACM, n.d. https://doi.org/10.1145/3297280.3297322. ieee: K. Chatterjee, A. K. Goharshady, and E. K. Goharshady, “The treewidth of smart contracts,” in Proceedings of the 34th ACM Symposium on Applied Computing, Limassol, Cyprus, vol. Part F147772, pp. 400–408. ista: 'Chatterjee K, Goharshady AK, Goharshady EK. The treewidth of smart contracts. Proceedings of the 34th ACM Symposium on Applied Computing. SAC: Symposium on Applied Computing vol. Part F147772, 400–408.' mla: Chatterjee, Krishnendu, et al. “The Treewidth of Smart Contracts.” Proceedings of the 34th ACM Symposium on Applied Computing, vol. Part F147772, ACM, pp. 400–08, doi:10.1145/3297280.3297322. short: K. Chatterjee, A.K. Goharshady, E.K. Goharshady, in:, Proceedings of the 34th ACM Symposium on Applied Computing, ACM, n.d., pp. 400–408. conference: end_date: 2019-04-12 location: Limassol, Cyprus name: 'SAC: Symposium on Applied Computing' start_date: 2019-04-08 date_created: 2019-05-26T21:59:15Z date_published: 2019-04-01T00:00:00Z date_updated: 2024-03-27T23:30:33Z day: '01' ddc: - '000' department: - _id: KrCh doi: 10.1145/3297280.3297322 external_id: isi: - '000474685800052' file: - access_level: open_access checksum: dddc20f6d9881f23b8755eb720ec9d6f content_type: application/pdf creator: dernst date_created: 2020-05-14T09:50:11Z date_updated: 2020-07-14T12:47:32Z file_id: '7827' file_name: 2019_ACM_Chatterjee.pdf file_size: 6937138 relation: main_file file_date_updated: 2020-07-14T12:47:32Z has_accepted_license: '1' isi: 1 language: - iso: eng month: '04' oa: 1 oa_version: Submitted Version page: 400-408 publication: Proceedings of the 34th ACM Symposium on Applied Computing publication_identifier: isbn: - '9781450359337' publication_status: submitted publisher: ACM pubrep_id: '1070' quality_controlled: '1' related_material: record: - id: '8934' relation: dissertation_contains status: public scopus_import: '1' status: public title: The treewidth of smart contracts type: conference user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: Part F147772 year: '2019' ... --- _id: '7158' abstract: - lang: eng text: "Interprocedural analysis is at the heart of numerous applications in programming languages, such as alias analysis, constant propagation, and so on. Recursive state machines (RSMs) are standard models for interprocedural analysis. We consider a general framework with RSMs where the transitions are labeled from a semiring and path properties are algebraic with semiring operations. RSMs with algebraic path properties can model interprocedural dataflow analysis problems, the shortest path problem, the most probable path problem, and so on. The traditional algorithms for interprocedural analysis focus on path properties where the starting point is fixed as the entry point of a specific method. In this work, we consider possible multiple queries as required in many applications such as in alias analysis. The study of multiple queries allows us to bring in an important algorithmic distinction between the resource usage of the one-time preprocessing vs for each individual query. The second aspect we consider is that the control flow graphs for most programs have constant treewidth.\r\n\r\nOur main contributions are simple and implementable algorithms that support multiple queries for algebraic path properties for RSMs that have constant treewidth. Our theoretical results show that our algorithms have small additional one-time preprocessing but can answer subsequent queries significantly faster as compared to the current algorithmic solutions for interprocedural dataflow analysis. We have also implemented our algorithms and evaluated their performance for performing on-demand interprocedural dataflow analysis on various domains, such as for live variable analysis and reaching definitions, on a standard benchmark set. Our experimental results align with our theoretical statements and show that after a lightweight preprocessing, on-demand queries are answered much faster than the standard existing algorithmic approaches.\r\n" article_number: '23' article_processing_charge: No article_type: original author: - first_name: Krishnendu full_name: Chatterjee, Krishnendu id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87 last_name: Chatterjee orcid: 0000-0002-4561-241X - first_name: Amir Kafshdar full_name: Goharshady, Amir Kafshdar id: 391365CE-F248-11E8-B48F-1D18A9856A87 last_name: Goharshady orcid: 0000-0003-1702-6584 - first_name: Prateesh full_name: Goyal, Prateesh last_name: Goyal - first_name: Rasmus full_name: Ibsen-Jensen, Rasmus id: 3B699956-F248-11E8-B48F-1D18A9856A87 last_name: Ibsen-Jensen orcid: 0000-0003-4783-0389 - first_name: Andreas full_name: Pavlogiannis, Andreas id: 49704004-F248-11E8-B48F-1D18A9856A87 last_name: Pavlogiannis orcid: 0000-0002-8943-0722 citation: ama: Chatterjee K, Goharshady AK, Goyal P, Ibsen-Jensen R, Pavlogiannis A. Faster algorithms for dynamic algebraic queries in basic RSMs with constant treewidth. ACM Transactions on Programming Languages and Systems. 2019;41(4). doi:10.1145/3363525 apa: Chatterjee, K., Goharshady, A. K., Goyal, P., Ibsen-Jensen, R., & Pavlogiannis, A. (2019). Faster algorithms for dynamic algebraic queries in basic RSMs with constant treewidth. ACM Transactions on Programming Languages and Systems. ACM. https://doi.org/10.1145/3363525 chicago: Chatterjee, Krishnendu, Amir Kafshdar Goharshady, Prateesh Goyal, Rasmus Ibsen-Jensen, and Andreas Pavlogiannis. “Faster Algorithms for Dynamic Algebraic Queries in Basic RSMs with Constant Treewidth.” ACM Transactions on Programming Languages and Systems. ACM, 2019. https://doi.org/10.1145/3363525. ieee: K. Chatterjee, A. K. Goharshady, P. Goyal, R. Ibsen-Jensen, and A. Pavlogiannis, “Faster algorithms for dynamic algebraic queries in basic RSMs with constant treewidth,” ACM Transactions on Programming Languages and Systems, vol. 41, no. 4. ACM, 2019. ista: Chatterjee K, Goharshady AK, Goyal P, Ibsen-Jensen R, Pavlogiannis A. 2019. Faster algorithms for dynamic algebraic queries in basic RSMs with constant treewidth. ACM Transactions on Programming Languages and Systems. 41(4), 23. mla: Chatterjee, Krishnendu, et al. “Faster Algorithms for Dynamic Algebraic Queries in Basic RSMs with Constant Treewidth.” ACM Transactions on Programming Languages and Systems, vol. 41, no. 4, 23, ACM, 2019, doi:10.1145/3363525. short: K. Chatterjee, A.K. Goharshady, P. Goyal, R. Ibsen-Jensen, A. Pavlogiannis, ACM Transactions on Programming Languages and Systems 41 (2019). date_created: 2019-12-09T08:33:33Z date_published: 2019-11-01T00:00:00Z date_updated: 2024-03-27T23:30:34Z day: '01' ddc: - '000' department: - _id: KrCh doi: 10.1145/3363525 ec_funded: 1 external_id: isi: - '000564108400004' file: - access_level: open_access checksum: 291cc86a07bd010d4815e177dac57b70 content_type: application/pdf creator: dernst date_created: 2020-10-08T12:58:10Z date_updated: 2020-10-08T12:58:10Z file_id: '8632' file_name: 2019_ACMTransactions_Chatterjee.pdf file_size: 667357 relation: main_file success: 1 file_date_updated: 2020-10-08T12:58:10Z has_accepted_license: '1' intvolume: ' 41' isi: 1 issue: '4' language: - iso: eng month: '11' oa: 1 oa_version: Submitted Version project: - _id: 2584A770-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P 23499-N23 name: Modern Graph Algorithmic Techniques in Formal Verification - _id: 25863FF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: S11407 name: Game Theory - _id: 2581B60A-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '279307' name: 'Quantitative Graph Games: Theory and Applications' publication: ACM Transactions on Programming Languages and Systems publication_identifier: issn: - 0164-0925 publication_status: published publisher: ACM quality_controlled: '1' related_material: record: - id: '8934' relation: dissertation_contains status: public scopus_import: '1' status: public title: Faster algorithms for dynamic algebraic queries in basic RSMs with constant treewidth type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 41 year: '2019' ... --- _id: '7014' abstract: - lang: eng text: "We study the problem of developing efficient approaches for proving\r\nworst-case bounds of non-deterministic recursive programs. Ranking functions\r\nare sound and complete for proving termination and worst-case bounds of\r\nnonrecursive programs. First, we apply ranking functions to recursion,\r\nresulting in measure functions. We show that measure functions provide a sound\r\nand complete approach to prove worst-case bounds of non-deterministic recursive\r\nprograms. Our second contribution is the synthesis of measure functions in\r\nnonpolynomial forms. We show that non-polynomial measure functions with\r\nlogarithm and exponentiation can be synthesized through abstraction of\r\nlogarithmic or exponentiation terms, Farkas' Lemma, and Handelman's Theorem\r\nusing linear programming. While previous methods obtain worst-case polynomial\r\nbounds, our approach can synthesize bounds of the form $\\mathcal{O}(n\\log n)$\r\nas well as $\\mathcal{O}(n^r)$ where $r$ is not an integer. We present\r\nexperimental results to demonstrate that our approach can obtain efficiently\r\nworst-case bounds of classical recursive algorithms such as (i) Merge-Sort, the\r\ndivide-and-conquer algorithm for the Closest-Pair problem, where we obtain\r\n$\\mathcal{O}(n \\log n)$ worst-case bound, and (ii) Karatsuba's algorithm for\r\npolynomial multiplication and Strassen's algorithm for matrix multiplication,\r\nwhere we obtain $\\mathcal{O}(n^r)$ bound such that $r$ is not an integer and\r\nclose to the best-known bounds for the respective algorithms." article_number: '20' article_processing_charge: No article_type: original author: - first_name: Krishnendu full_name: Chatterjee, Krishnendu id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87 last_name: Chatterjee orcid: 0000-0002-4561-241X - first_name: Hongfei full_name: Fu, Hongfei last_name: Fu - first_name: Amir Kafshdar full_name: Goharshady, Amir Kafshdar id: 391365CE-F248-11E8-B48F-1D18A9856A87 last_name: Goharshady orcid: 0000-0003-1702-6584 citation: ama: Chatterjee K, Fu H, Goharshady AK. Non-polynomial worst-case analysis of recursive programs. ACM Transactions on Programming Languages and Systems. 2019;41(4). doi:10.1145/3339984 apa: Chatterjee, K., Fu, H., & Goharshady, A. K. (2019). Non-polynomial worst-case analysis of recursive programs. ACM Transactions on Programming Languages and Systems. ACM. https://doi.org/10.1145/3339984 chicago: Chatterjee, Krishnendu, Hongfei Fu, and Amir Kafshdar Goharshady. “Non-Polynomial Worst-Case Analysis of Recursive Programs.” ACM Transactions on Programming Languages and Systems. ACM, 2019. https://doi.org/10.1145/3339984. ieee: K. Chatterjee, H. Fu, and A. K. Goharshady, “Non-polynomial worst-case analysis of recursive programs,” ACM Transactions on Programming Languages and Systems, vol. 41, no. 4. ACM, 2019. ista: Chatterjee K, Fu H, Goharshady AK. 2019. Non-polynomial worst-case analysis of recursive programs. ACM Transactions on Programming Languages and Systems. 41(4), 20. mla: Chatterjee, Krishnendu, et al. “Non-Polynomial Worst-Case Analysis of Recursive Programs.” ACM Transactions on Programming Languages and Systems, vol. 41, no. 4, 20, ACM, 2019, doi:10.1145/3339984. short: K. Chatterjee, H. Fu, A.K. Goharshady, ACM Transactions on Programming Languages and Systems 41 (2019). date_created: 2019-11-13T08:33:43Z date_published: 2019-10-01T00:00:00Z date_updated: 2024-03-27T23:30:33Z day: '01' department: - _id: KrCh doi: 10.1145/3339984 ec_funded: 1 external_id: arxiv: - '1705.00317' isi: - '000564108400001' intvolume: ' 41' isi: 1 issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1705.00317 month: '10' oa: 1 oa_version: Preprint project: - _id: 25892FC0-B435-11E9-9278-68D0E5697425 grant_number: ICT15-003 name: Efficient Algorithms for Computer Aided Verification - _id: 25832EC2-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: S 11407_N23 name: Rigorous Systems Engineering - _id: 2581B60A-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '279307' name: 'Quantitative Graph Games: Theory and Applications' - _id: 267066CE-B435-11E9-9278-68D0E5697425 name: Quantitative Analysis of Probablistic Systems with a focus on Crypto-currencies - _id: 266EEEC0-B435-11E9-9278-68D0E5697425 name: Quantitative Game-theoretic Analysis of Blockchain Applications and Smart Contracts publication: ACM Transactions on Programming Languages and Systems publication_status: published publisher: ACM quality_controlled: '1' related_material: record: - id: '639' relation: earlier_version status: public - id: '8934' relation: dissertation_contains status: public scopus_import: '1' status: public title: Non-polynomial worst-case analysis of recursive programs type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 41 year: '2019' ...