{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T15:08:04Z","timestamp":1774451284875,"version":"3.50.1"},"publisher-location":"Cham","reference-count":49,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783030524814","type":"print"},{"value":"9783030524821","type":"electronic"}],"license":[{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020]]},"DOI":"10.1007\/978-3-030-52482-1_1","type":"book-chapter","created":{"date-parts":[[2020,7,8]],"date-time":"2020-07-08T16:03:46Z","timestamp":1594224226000},"page":"3-32","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Inverse Problems, Constraint Satisfaction, Reversible Logic, Invertible Logic and Grover Quantum Oracles for Practical Problems"],"prefix":"10.1007","author":[{"given":"Marek","family":"Perkowski","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,7,9]]},"reference":[{"issue":"10","key":"1_CR1","doi-asserted-by":"publisher","first-page":"2588","DOI":"10.1109\/TVLSI.2017.2654298","volume":"25","author":"A Ardakani","year":"2017","unstructured":"Ardakani, A., Leduc-Primeau, F., Onizawa, N., Hanyu, T., Gross, W.J.: VLSI implementation of deep neural network using integral stochastic computing. IEEE Trans. Very Large Scale Integr. (VLSI) Syst. 25(10), 2588\u20132599 (2017)","journal-title":"IEEE Trans. Very Large Scale Integr. (VLSI) Syst."},{"key":"1_CR2","unstructured":"Cheng, A., Tsai, E., Perkowski, M.: Methodology to create hardware oracles for solving constraint satisfaction problems. In: 22nd International Workshop on Post-Binary ULSI Systems, pp. 36\u201343. Toyama International Conference Center, Toyama (2013)"},{"key":"1_CR3","doi-asserted-by":"publisher","unstructured":"Dhawan, S., Perkowski, M.: Comparison of influence of two data-encoding methods for grover algorithm on quantum costs. In: ISMVL, pp. 176\u2013181 (2011). \nhttps:\/\/doi.org\/10.1109\/ismvl.2011.29","DOI":"10.1109\/ismvl.2011.29"},{"key":"1_CR4","doi-asserted-by":"publisher","first-page":"052331","DOI":"10.1103\/PhysRevA.77.052331","volume":"77","author":"JD Biamonte","year":"2008","unstructured":"Biamonte, J.D.: Non-perturbative k-body to two-body commuting conversion Hamiltonians and embedding problem instances into Ising spins. Phys. Rev. A 77, 052331 (2008)","journal-title":"Phys. Rev. A"},{"key":"1_CR5","first-page":"031014","volume":"7","author":"K Camsari","year":"2017","unstructured":"Camsari, K., Faria, R., Sutton, B., Datta, S.: Stochastic p-bits for invertible logic. Phys. Rev. X 7, 031014 (2017)","journal-title":"Phys. Rev. X"},{"key":"1_CR6","doi-asserted-by":"crossref","unstructured":"Debashis, P., Faria, R., Camsari, K.Y., Appenzeller, J., Datta, S., Chen, Z.: Experimental demonstration of nanomagnet networks as hardware for Ising computing. In: IEEE International Electron Devices Meeting (IEDM), pp. 34.3.1\u201334.3.4 (2016)","DOI":"10.1109\/IEDM.2016.7838539"},{"key":"1_CR7","series-title":"Advances in Information Systems Science","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1007\/978-1-4899-5841-9_2","volume-title":"Advances in Information Systems Science","author":"BR Gaines","year":"1969","unstructured":"Gaines, B.R.: Stochastic computing systems. In: Tou, J.T. (ed.) Advances in Information Systems Science. Advances in Information Systems Science, pp. 37\u2013172. Springer, Boston (1969). \nhttps:\/\/doi.org\/10.1007\/978-1-4899-5841-9_2"},{"issue":"5&6","key":"1_CR8","first-page":"0417","volume":"20","author":"P Gao","year":"2020","unstructured":"Gao, P., Li, Y., Perkowski, M., Song, X.: Realization of quantum oracles using symmetries of Boolean functions. Quantum Inf. Comput. 20(5&6), 0417\u20130446 (2020)","journal-title":"Quantum Inf. Comput."},{"key":"1_CR9","doi-asserted-by":"crossref","unstructured":"Grover, L.K.: A fast quantum mechanical algorithm for database search. In: 28th Annual ACM Symposium on Theory of Computing, pp. 212\u2013219 (1996)","DOI":"10.1145\/237814.237866"},{"key":"1_CR10","unstructured":"Hinton, G.E., Sejnowski, T.J., Ackley, D.H.: Boltzmann machines: constraint satisfaction networks that learn. Department of Computer Science, Carnegie-Mellon University, Technical report CMUCS-84-119 (1984)"},{"key":"1_CR11","doi-asserted-by":"crossref","unstructured":"Lee, B., Perkowski, M.: Quantum machine learning based on minimizing Kronecker-Reed-Muller forms and Grover search algorithm with hybrid oracles. In: 2016 Euromicro Conference on Digital System Design (DSD), pp. 413\u2013422 (2016)","DOI":"10.1109\/DSD.2016.30"},{"issue":"1&2","key":"1_CR12","first-page":"0035","volume":"19","author":"Y Li","year":"2019","unstructured":"Li, Y., Tsai, Y., Perkowski, M., Song, X.: Grover-based Ashenhurst-Curtis decomposition using quantum language quipper. Quantum Inf. Comput. 19(1&2), 0035\u20130066 (2019)","journal-title":"Quantum Inf. Comput."},{"key":"1_CR13","unstructured":"Mishchenko, A., Perkowski, M.: Fast heuristic minimization of exclusive sums-of-products. In: RM 2001 Workshop (2001)"},{"issue":"3","key":"1_CR14","doi-asserted-by":"publisher","first-page":"1051","DOI":"10.1109\/TCSI.2017.2771533","volume":"65","author":"JV Monaco","year":"2018","unstructured":"Monaco, J.V., Vindiola, M.M.: Factoring integers with a brain-inspired computer. IEEE Trans. Circuits Syst. I Regul. Pap. 65(3), 1051\u20131062 (2018)","journal-title":"IEEE Trans. Circuits Syst. I Regul. Pap."},{"key":"1_CR15","unstructured":"Perkowski, M.: Methodology to design oracles for Grover algorithm, poster presentation. In: Workshop on Design Automation for Quantum Computers, IEEE 2017 International Conference On Computer Aided Design, Marriott Hotel, Irvine, CA (2017)"},{"issue":"3\u20134","key":"1_CR16","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1155\/1995\/67208","volume":"3","author":"T Luba","year":"1995","unstructured":"Luba, T., Selvaraj, H.: A general approach to Boolean function decomposition and its application in FPGA based synthesis. VLSI Des. 3(3\u20134), 289\u2013300 (1995)","journal-title":"VLSI Des."},{"key":"1_CR17","unstructured":"Pervaiz, A.Z., Ghantasala, L.A., Camsari, K., Datta, S.: Hardware emulation of stochastic p-bits for invertible logic. Sci. Rep. 7 (2017). Article No. 10994"},{"key":"1_CR18","unstructured":"Pervaiz, A.Z., Sutton, B.M., Ghantasala, L.A., Camsari, K.Y.: Weighted p-bits for FPGA implementation of probabilistic circuits. arXiv e-prints (2017)"},{"key":"1_CR19","doi-asserted-by":"publisher","first-page":"1484","DOI":"10.1137\/S0097539795293172","volume":"26","author":"PW Shor","year":"1997","unstructured":"Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26, 1484\u20131509 (1997)","journal-title":"SIAM J. Comput."},{"issue":"6","key":"1_CR20","doi-asserted-by":"publisher","first-page":"2263","DOI":"10.1109\/TCSI.2018.2889732","volume":"66","author":"SC Smithson","year":"2019","unstructured":"Smithson, S.C., Onizawa, N., Meyer, B.H., Gross, W.J., Hanyu, T.: Efficient CMOS invertible logic using stochastic computing. IEEE Trans. Circuits Syst. I Regul. Pap. 66(6), 2263\u20132274 (2019)","journal-title":"IEEE Trans. Circuits Syst. I Regul. Pap."},{"key":"1_CR21","first-page":"169","volume":"33","author":"E Tsai","year":"2020","unstructured":"Tsai, E., Perkowski, M.: A quantum algorithm for automata encoding. Facta Universitatis. Ser. Electron. Energ. 33, 169\u2013215 (2020)","journal-title":"Ser. Electron. Energ."},{"key":"1_CR22","unstructured":"Tsai, E., Perkowski, M.: Towards the Development of Quantum Design Automation Tools: A Methodology for Construction of Oracles to Solve Constraint Satisfaction Problems using Grover\u2019s Algorithm (2020, Submitted)"},{"key":"1_CR23","unstructured":"Tsai, E., Perkowski, M.: Realization of Arbitrary Symmetric Functions in Quantum Logic Using Two-Qubit Gate (2020, Submitted)"},{"key":"1_CR24","doi-asserted-by":"publisher","unstructured":"Wang, Y., Perkowski, M.: Improved complexity of quantum oracles for ternary Grover algorithm for graph coloring. In: ISMVL, pp. 294\u2013301 (2011). \nhttps:\/\/doi.org\/10.1109\/ismvl.2011.42","DOI":"10.1109\/ismvl.2011.42"},{"issue":"5","key":"1_CR25","doi-asserted-by":"publisher","first-page":"57004","DOI":"10.1209\/0295-5075\/99\/57004","volume":"99","author":"JD Whitfield","year":"2012","unstructured":"Whitfield, J.D., Faccin, M., Biamonte, J.D.: Ground-state spin logic. Europhys. Lett. 99(5), 57004 (2012)","journal-title":"Europhys. Lett."},{"key":"1_CR26","unstructured":"Butler, J.T., Sasao, T.: Combinational computing. One object per clock. In: Reed-Muller Symposium, Toyama, Japan (2013)"},{"issue":"1","key":"1_CR27","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/srep44370","volume":"7","author":"B Sutton","year":"2017","unstructured":"Sutton, B., Camsari, K.Y., Behin-Aein, B., Datta, S.: Intrinsic optimization using stochastic nanomagnets. Sci. Rep. 7(1), 1\u20139 (2017)","journal-title":"Sci. Rep."},{"key":"1_CR28","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"820","DOI":"10.1007\/BFb0055105","volume-title":"Automata, Languages and Programming","author":"G Brassard","year":"1998","unstructured":"Brassard, G., H\u00d8yer, P., Tapp, A.: Quantum counting. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 820\u2013831. Springer, Heidelberg (1998). \nhttps:\/\/doi.org\/10.1007\/BFb0055105"},{"key":"1_CR29","doi-asserted-by":"crossref","unstructured":"Venkatachalapathy, R.: Systems isomorphisms in stochastic dynamic systems. PSU, Systems Science, Ph.D. Dissertation (2019)","DOI":"10.15760\/etd.7283"},{"key":"1_CR30","unstructured":"Sivakumar, S., Li, Y., Perkowski, M.: Grover Algorithm for Minimum Set of Support Problem of Multi-Valued Functions (2020, Submitted)"},{"key":"1_CR31","unstructured":"Zhang, W.: Quantum Algorithms for Two-Arm robot and generalization to Travelling Salesman Problem (2020, in Preparation)"},{"key":"1_CR32","unstructured":"Hou, W., Perkowski, M.: Quantum Algorithm for Knapsack problem (2020, Submitted)"},{"key":"1_CR33","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1016\/S1383-7621(00)00062-X","volume":"47","author":"M Rawski","year":"2001","unstructured":"Rawski, M., J\u00f3\u017awiak, L., Luba, T.: Functional decomposition with an efficient input support selection for sub-functions based on information relationship measures. J. Syst. Architect. 47, 137\u2013155 (2001)","journal-title":"J. Syst. Architect."},{"key":"1_CR34","unstructured":"Konieczny, P.A., J\u00f3\u017awiak, L.: Minimal input support problem and algorithms to solve it, vol. 95-E-289. Eindhoven University of Technology Report E, Faculty of Electrical Engineering, Eindhoven, 01 January 1995"},{"key":"1_CR35","unstructured":"Mishchenko, A., Files, C., Perkowski, M., Steinbach, B., Dorotska, C.: Implicit algorithms for multi-valued input support manipulation. In: 4th International Workshop on Boolean Problems (2000)"},{"key":"1_CR36","unstructured":"Kiran, R.U., Reddy, P.K.: An improved multiple minimum support based approach to mine rare association rules. IEEE (2009). 978-1-4244-2765-9\/09"},{"issue":"3\u20134","key":"1_CR37","first-page":"241","volume":"18","author":"T \u0141uba","year":"1993","unstructured":"\u0141uba, T., Rybnik, J.: Algorithmic approach to discernibility function with respect to attributes and objects reduction. Found. Comput. Decis. Sci. 18(3\u20134), 241\u2013258 (1993)","journal-title":"Found. Comput. Decis. Sci."},{"key":"1_CR38","first-page":"1","volume":"38","author":"T Sasao","year":"2015","unstructured":"Sasao, T., Fumishi, I., Iguchi, Y.: On an exact minimization of variables for incompletely specified index generation functions using SAT. Note Multiple-Valued Logic Jpn. 38, 1\u20138 (2015)","journal-title":"Note Multiple-Valued Logic Jpn."},{"key":"1_CR39","volume-title":"Quantum Computation and Quantum Information","author":"MA Nielsen","year":"2000","unstructured":"Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)"},{"key":"1_CR40","doi-asserted-by":"publisher","first-page":"493","DOI":"10.1002\/(SICI)1521-3978(199806)46:4\/5<493::AID-PROP493>3.0.CO;2-P","volume":"46","author":"M Boyer","year":"1998","unstructured":"Boyer, M., Brassard, G., H\u00f8yer, P., Tapp, A.: Tight bounds on quantum searching. Fortschr. Phys. 46, 493 (1998)","journal-title":"Fortschr. Phys."},{"key":"1_CR41","unstructured":"Cross, A.: The IBM Q experience and QISKit open-source quantum computing software. APS March Meeting (2018). Abstract id L58.003. Bibcode 2018 APS .. MARL58003C"},{"key":"1_CR42","unstructured":"Al-Bayaty, A., Perkowski, M.: Simulating Boolean, Quantum and Invertible Logic Oracles using a Prolog-based system. Report PSU (2020, in Preparation)"},{"key":"1_CR43","doi-asserted-by":"crossref","unstructured":"Taha, M.M.A., Perkowski, M.: Realization of arithmetic operators based on stochastic number frequency signal representation. In: ISMVL 2018, pp. 215\u2013220 (2018)","DOI":"10.1109\/ISMVL.2018.00045"},{"key":"1_CR44","unstructured":"Cheng, A.: Designing FPGA Oracles for Cryptography Problems. PSU report (2013)"},{"key":"1_CR45","unstructured":"Li, Y.: Quantum Oracles for Graph Coloring and Maximum Clique. PSU report in preparation (2020)"},{"issue":"3","key":"1_CR46","first-page":"52","volume":"22","author":"M Perkowski","year":"2002","unstructured":"Perkowski, M., Foote, D., Chen, Q., Al-Rabadi, A., Jozwiak, L.: Learning hardware using multiple-valued logic \u2013 Part 2: cube calculus and architecture. IEEE Micro Chips Syst. Softw. Appl. 22(3), 52\u201361 (2002)","journal-title":"IEEE Micro Chips Syst. Softw. Appl."},{"key":"1_CR47","volume-title":"Switching and Finite Automata Theory","author":"Z Kohavi","year":"1978","unstructured":"Kohavi, Z.: Switching and Finite Automata Theory. McGraw-Hill, New York (1978)"},{"key":"1_CR48","doi-asserted-by":"crossref","unstructured":"Preskill, J.: Quantum computing in the NISQ era and beyond. \narXiv:1801.00862v3\n\n [quant-ph], 31 July 2018","DOI":"10.22331\/q-2018-08-06-79"},{"key":"1_CR49","first-page":"353","volume-title":"Progress in Computer Aided VLSI Design","author":"M Perkowski","year":"1989","unstructured":"Perkowski, M., Liu, J., Brown, J.: Quick software prototyping: CAD design of digital CAD algorithms. In: Zobrist, G. (ed.) Progress in Computer Aided VLSI Design, vol. 1, pp. 353\u2013401. Ablex Publishing Corp, New York (1989)"}],"container-title":["Lecture Notes in Computer Science","Reversible Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-52482-1_1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,7,8]],"date-time":"2020-07-08T17:06:37Z","timestamp":1594227997000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-030-52482-1_1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020]]},"ISBN":["9783030524814","9783030524821"],"references-count":49,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-52482-1_1","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020]]},"assertion":[{"value":"9 July 2020","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"RC","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Reversible Computation","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Oslo","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Norway","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2020","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"9 July 2020","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"10 July 2020","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"12","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"rc2020","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/www.revcomp.eu\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Double-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Easychair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"22","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"11","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"0","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"50% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"2","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"The conference was held virtually due to the COVID-19 pandemic.","order":10,"name":"additional_info_on_review_process","label":"Additional Info on Review Process","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}