Dichotomy for Holant∗ Problems on the Boolean Domain
Holant problems are a general framework to study counting problems. Both counting constraint satisfaction problems (#CSP) and graph homomorphisms are special cases. We prove a complexity dichotomy theorem for Holant ∗ ( F ) , where F is a set of constraint functions on Boolean variables and taking c...
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| Vydáno v: | Theory of computing systems Ročník 64; číslo 8; s. 1362 - 1391 |
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| Abstract | Holant problems are a general framework to study counting problems. Both counting constraint satisfaction problems (#CSP) and graph homomorphisms are special cases. We prove a complexity dichotomy theorem for
Holant
∗
(
F
)
, where
F
is a set of constraint functions on Boolean variables and taking complex values. The constraint functions need not be symmetric functions. We identify four classes of problems which are polynomial time computable; all other problems are proved to be #P-hard. The main proof technique and indeed the formulation of the theorem use holographic algorithms and reductions. By considering these counting problems with the broader scope that allows complex-valued constraint functions, we discover surprising new tractable classes, which are associated with isotropic vectors, i.e., a (non-zero) vector whose dot product with itself is zero. |
|---|---|
| AbstractList | Holant problems are a general framework to study counting problems. Both counting constraint satisfaction problems (#CSP) and graph homomorphisms are special cases. We prove a complexity dichotomy theorem for
Holant
∗
(
F
)
, where
F
is a set of constraint functions on Boolean variables and taking complex values. The constraint functions need not be symmetric functions. We identify four classes of problems which are polynomial time computable; all other problems are proved to be #P-hard. The main proof technique and indeed the formulation of the theorem use holographic algorithms and reductions. By considering these counting problems with the broader scope that allows complex-valued constraint functions, we discover surprising new tractable classes, which are associated with isotropic vectors, i.e., a (non-zero) vector whose dot product with itself is zero. Holant problems are a general framework to study counting problems. Both counting constraint satisfaction problems (#CSP) and graph homomorphisms are special cases. We prove a complexity dichotomy theorem for Holant∗(F), where F is a set of constraint functions on Boolean variables and taking complex values. The constraint functions need not be symmetric functions. We identify four classes of problems which are polynomial time computable; all other problems are proved to be #P-hard. The main proof technique and indeed the formulation of the theorem use holographic algorithms and reductions. By considering these counting problems with the broader scope that allows complex-valued constraint functions, we discover surprising new tractable classes, which are associated with isotropic vectors, i.e., a (non-zero) vector whose dot product with itself is zero. |
| Author | Lu, Pinyan Cai, Jin-Yi Xia, Mingji |
| Author_xml | – sequence: 1 givenname: Jin-Yi surname: Cai fullname: Cai, Jin-Yi email: jyc@cs.wisc.edu organization: Computer Sciences Department, University of Wisconsin-Madison – sequence: 2 givenname: Pinyan surname: Lu fullname: Lu, Pinyan organization: School of Information Management and Engineering, Shanghai University of Finance and Economics – sequence: 3 givenname: Mingji surname: Xia fullname: Xia, Mingji organization: Stake Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, University of Chinese Academy of Sciences |
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| Cites_doi | 10.1145/2371656.2371660 10.1016/0031-8914(61)90063-5 10.4159/harvard.9780674180758 10.1017/9781107477063 10.1103/PhysRev.87.410 10.1137/1.9781611975482.30 10.1137/070690201 10.1109/FOCS.2014.70 10.1016/j.jcss.2010.06.005 10.1007/BF02280291 10.1145/321864.321877 10.1137/110840194 10.1145/1806689.1806789 10.1137/0222066 10.1109/FOCS.2008.34 10.1109/FOCS.2006.7 10.1137/070682575 10.1103/PhysRev.65.117 10.1080/14786436108243366 10.1137/1.9781611975031.118 10.1137/1.9781611973082.132 10.1145/800133.804350 10.1007/BF01213009 10.1017/CBO9780511752506 10.1137/090757496 10.1103/PhysRev.87.404 10.1109/FOCS.2010.49 10.1214/aoap/1026915617 10.1145/1536414.1536511 10.1137/1.9781611973105.93 10.1006/inco.1996.0016 10.1137/1.9780898718546 10.1016/j.jcss.2011.12.002 10.1016/j.tcs.2005.09.011 10.1016/j.jcss.2009.08.003 10.1137/S0097539700377025 10.1103/PhysRev.85.808 10.1145/1314690.1314691 10.1016/0095-8956(90)90132-J 10.1090/S0894-0347-07-00568-1 |
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| Keywords | P-hardness Constraint satisfaction problems Dichotomy theorems Edge coloring models Holant problems Polynomial time algorithms |
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| References | BulatovAAGroheMThe complexity of partition functionsTheor. Comput. Sci.20053482-3148186218137410.1016/j.tcs.2005.09.011 Cai, J., Chen, X.: A Decidable Dichotomy Theorem on Directed Graph Homomorphisms with Non-Negative Weights. In: 51Th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2010, pp 437–446. IEEE Computer Society, Las Vegas (2010) KasteleynPWThe statistics of dimers on a latticePhysica1961271209122510.1016/0031-8914(61)90063-5 CreignouNHermannMComplexity of generalized satisfiability counting problemsInf. Comput.19961251112138580410.1006/inco.1996.0016 Cai, J., Lu, P., Xia, M.: Dichotomy for Holant* problems with domain size 3. In: Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2013, pp. 1278–1295, New Orleans (2013) ValiantLGQuantum circuits that can be simulated classically in polynomial timeSIAM J. Comput.200231412291254191996410.1137/S0097539700377025 GoldbergLAJerrumMApproximating the partition function of the ferromagnetic potts modelJ. ACM201259525:125:31299582410.1145/2371656.2371660 Randall, D.: Mixing. In: 44Th Symposium on Foundations of Computer Science (FOCS 2003), 11-14 October 2003, Cambridge, MA, USA, Proceedings, pp. 4–15 (2003) Dyer, M. E., Richerby, D.: On the complexity of #CSP. In: Schulman, L.J. (ed.) Proceedings of the 42nd ACM Symposium on Theory of Computing, STOC 2010, pp 725–734. ACM, Cambridge (2010) OnsagerLCrystal statistics. i. a two-dimensional model with an order-disorder transitionPhys. Rev.1944653-41171491031510.1103/PhysRev.65.117 MadrasNRandallDMarkov chain decomposition for convergence rate analysisAnn. Appl. Probab.2002122581606191064110.1214/aoap/1026915617 LadnerREOn the structure of polynomial time reducibilityJ. ACM197522115517146469810.1145/321864.321877 DyerMEGoldbergLAJerrumMAn approximation trichotomy for Boolean #CSPJ. Comput. Syst. Sci.2010763-4267277265649210.1016/j.jcss.2009.08.003 BulatovAAThe complexity of the counting constraint satisfaction problemJ. ACM201360534:134:4131246831281.68130 LiebESokalAA general Lee-Yang theorem for one-component and multicomponent ferromagnetsCommun. Math. Phys.198180215317962315610.1007/BF01213009 YangCLeeTStatistical theory of equations of state and phase transitions. I. Theory of condensationPhys. Rev.19528734044095302810.1103/PhysRev.87.404 BaxterRJExactly solved models in statistical mechanics1982LondonAcademic Press0538.60093 Valiant, L. G.: Accidental algorthims. In: FOCS ’06: Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science. https://doi.org/10.1109/FOCS.2006.7, pp 509–517. IEEE Computer Society, Washington (2006) CaiJLuPHolographic algorithms: From art to scienceJ. Comput. Syst. Sci.20117714161276712410.1016/j.jcss.2010.06.005 McCoy, B., Wu, T.: The two-dimensional Ising model. Harvard University Press, Cambridge (1973) Kasteleyn, P. W.: Graph Theory and Crystal Physics. In: Harary, F. (ed.) Graph Theory and Theoretical Physics, pp 43–110. Academic Press, London (1967) Backens, M.: A New Holant Dichotomy Inspired by Quantum Computation. In: 44Th International Colloquium on Automata, Languages, and Programming, ICALP 2017, Warsaw, pp. 16:1–16:14 (2017) IsingEBeitrag zur theorie des ferromagnetismusZ. Phys. Hadrons Nucl.19253112532581439.82056 Cai, J. Y., Lu, P., Xia, M.: Holant Problems and Counting CSP. In: Mitzenmacher, M. (ed.) STOC, pp 715–724. ACM (2009) LovászLOperations with structuresActa Math. Hung.19671832132821452910.1007/BF02280291 ValiantLGHolographic algorithmsSIAM J. Comput.200837515651594238628110.1137/070682575https://doi.org/10.1137/070682575 Welsh, D.: Complexity: knots, colourings and counting. Cambridge University Press, Cambridge (1993) Cai, J., Chen, X.: Complexity dichotomies for counting problems. Cambridge University Press, Cambridge (2017) Creignou, N., Khanna, S., Sudan, M.: Complexity Classifications of Boolean Constraint Satisfaction Problems. Siam Monographs On Discrete Mathematics And Applications (2001) FreedmanMLovászLSchrijverAReflection positivity, rank connectivity, and homomorphism of graphsJ. AMS200720375122573961107.05089 SzegedyBEdge coloring models and reflection positivityJ. Amer. Math. Soc.200720969988232871210.1090/S0894-0347-07-00568-1 Dyer, M. E., Goldberg, L. A., Jalsenius, M., Richerby, D.: The Complexity of Approximating Bounded-Degree Boolean #CSP. In: Marion, J., Schwentick, T. (eds.) STACS, LIPIcs, vol. 5, pp 323–334. Schloss Dagstuhl - Leibniz-Zentrum fu̇r Informatik (2010) TemperleyHNVFisherMEDimer problem in statistical mechanics c an exact resultPhilos. Mag.196161061 C 106313639810.1080/14786436108243366 Cai, J., Lu, P., Xia, M.: Dichotomy for real Holantc problems. In: Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018, pp. 1802–1821, New Orleans (2018) JerrumMSinclairAPolynomial-time approximation algorithms for the ising modelSIAM J. Comput.199322510871116123716410.1137/0222066 Lin, J., Wang, H.: The Complexity of Holant Problems over Boolean Domain with Non-Negative Weights. In: 44Th International Colloquium on Automata, Languages, and Programming, ICALP 2017, pp 29:1–29:14, Warsaw (2017) Cai, J. Y., Lu, P., Xia, M.: Holographic algorithms by Fibonacci gates and holographic reductions for hardness. In: FOCS ’08: Proceedings of the 49th Annual IEEE Symposium on Foundations of Computer Science. IEEE Computer Society, Washington (2008) LeeTYangCStatistical theory of equations of state and phase transitions. II. Lattice gas and Ising modelPhys. Rev.19528734104195302910.1103/PhysRev.87.410 Cai, J., Lu, P., Xia, M.: Dichotomy for Holant* problems of Boolean domain. In: Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2011, pp. 1714–1728, San Francisco (2011) GoldbergLAGroheMJerrumMThurleyMA complexity dichotomy for partition functions with mixed signsSIAM J. Comput.201039733363402267807710.1137/090757496 Jerrum, M., Sinclair, A.: The Markov Chain Monte Carlo Method: an Approach to Approximate Counting and Integration. In: Approximation Algorithms for NP-Hard Problems, pp. 482–520. PWS Publishing (1996) Cai, J. Y., Govorov, A.: Perfect matchings, rank of connection tensors and graph homomorphisms. In: Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA ’19, pp. 476–495. Society for Industrial and Applied Mathematics, Philadelphia (2019) Backens, M.: A Complete Dichotomy for Complex-Valued Holantc. In: 45Th International Colloquium on Automata, Languages, and Programming, ICALP 2018, pp. 12:1–12:14 (2018) YangCThe spontaneous magnetization of a two-dimensional Ising modelPhys. Rev.19528558088165174010.1103/PhysRev.85.808 Cai, J., Guo, H., Williams, T.: The Complexity of Counting Edge Colorings and a Dichotomy for Some Higher Domain Holant Problems. In: 55Th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2014, pp. 601–610, Philadelphia (2014) CaiJChenXLuPGraph homomorphisms with complex values: a dichotomy theoremSIAM J. Comput.20134239241029305676410.1137/110840194 BulatovAADyerMEGoldbergLAJalseniusMJerrumMRicherbyDThe complexity of weighted and unweighted #CSPJ. Comput. Syst. Sci.2012782681688288135610.1016/j.jcss.2011.12.002 Schaefer, T. J.: The complexity of satisfiability problems. In: Proceedings of the 10th Annual ACM Symposium on Theory of Computing, pp. 216–226, San Diego (1978) DyerMEGoldbergLAJerrumMThe complexity of weighted Boolean #CSPSIAM J. Comput.200938519701986247628210.1137/070690201 HellPNešetřilJOn the complexity of H-coloringJ. Combin. Theory Ser. B199048192110104755510.1016/0095-8956(90)90132-J DyerMEGreenhillCSThe complexity of counting graph homomorphisms. Random StructAlgorithms2000173-426028918011350965.68073 Dyer, M. E., Goldberg, L. A., Paterson, M.: On counting homomorphisms to directed acyclic graphs. J. 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| References_xml | – reference: Valiant, L. G.: Accidental algorthims. In: FOCS ’06: Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science. https://doi.org/10.1109/FOCS.2006.7, pp 509–517. IEEE Computer Society, Washington (2006) – reference: GoldbergLAJerrumMApproximating the partition function of the ferromagnetic potts modelJ. ACM201259525:125:31299582410.1145/2371656.2371660 – reference: MadrasNRandallDMarkov chain decomposition for convergence rate analysisAnn. Appl. Probab.2002122581606191064110.1214/aoap/1026915617 – reference: Cai, J., Chen, X.: A Decidable Dichotomy Theorem on Directed Graph Homomorphisms with Non-Negative Weights. In: 51Th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2010, pp 437–446. IEEE Computer Society, Las Vegas (2010) – reference: Cai, J., Chen, X.: Complexity dichotomies for counting problems. Cambridge University Press, Cambridge (2017) – reference: DyerMEGoldbergLAJerrumMThe complexity of weighted Boolean #CSPSIAM J. Comput.200938519701986247628210.1137/070690201 – reference: JerrumMSinclairAPolynomial-time approximation algorithms for the ising modelSIAM J. Comput.199322510871116123716410.1137/0222066 – reference: Jerrum, M., Sinclair, A.: The Markov Chain Monte Carlo Method: an Approach to Approximate Counting and Integration. In: Approximation Algorithms for NP-Hard Problems, pp. 482–520. PWS Publishing (1996) – reference: CreignouNHermannMComplexity of generalized satisfiability counting problemsInf. Comput.19961251112138580410.1006/inco.1996.0016 – reference: OnsagerLCrystal statistics. i. a two-dimensional model with an order-disorder transitionPhys. Rev.1944653-41171491031510.1103/PhysRev.65.117 – reference: Creignou, N., Khanna, S., Sudan, M.: Complexity Classifications of Boolean Constraint Satisfaction Problems. Siam Monographs On Discrete Mathematics And Applications (2001) – reference: KasteleynPWThe statistics of dimers on a latticePhysica1961271209122510.1016/0031-8914(61)90063-5 – reference: Cai, J., Lu, P., Xia, M.: Dichotomy for Holant* problems of Boolean domain. In: Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2011, pp. 1714–1728, San Francisco (2011) – reference: Dyer, M. E., Richerby, D.: On the complexity of #CSP. In: Schulman, L.J. (ed.) Proceedings of the 42nd ACM Symposium on Theory of Computing, STOC 2010, pp 725–734. ACM, Cambridge (2010) – reference: CaiJChenXLuPGraph homomorphisms with complex values: a dichotomy theoremSIAM J. Comput.20134239241029305676410.1137/110840194 – reference: Dyer, M. E., Goldberg, L. A., Paterson, M.: On counting homomorphisms to directed acyclic graphs. J. ACM 54(6), 27:1–27:23 (2007) – reference: Dyer, M. E., Goldberg, L. A., Jalsenius, M., Richerby, D.: The Complexity of Approximating Bounded-Degree Boolean #CSP. In: Marion, J., Schwentick, T. (eds.) STACS, LIPIcs, vol. 5, pp 323–334. Schloss Dagstuhl - Leibniz-Zentrum fu̇r Informatik (2010) – reference: Randall, D.: Mixing. In: 44Th Symposium on Foundations of Computer Science (FOCS 2003), 11-14 October 2003, Cambridge, MA, USA, Proceedings, pp. 4–15 (2003) – reference: McCoy, B., Wu, T.: The two-dimensional Ising model. Harvard University Press, Cambridge (1973) – reference: CaiJLuPHolographic algorithms: From art to scienceJ. Comput. Syst. Sci.20117714161276712410.1016/j.jcss.2010.06.005 – reference: Lin, J., Wang, H.: The Complexity of Holant Problems over Boolean Domain with Non-Negative Weights. In: 44Th International Colloquium on Automata, Languages, and Programming, ICALP 2017, pp 29:1–29:14, Warsaw (2017) – reference: DyerMEGoldbergLAJerrumMAn approximation trichotomy for Boolean #CSPJ. Comput. Syst. Sci.2010763-4267277265649210.1016/j.jcss.2009.08.003 – reference: BulatovAAThe complexity of the counting constraint satisfaction problemJ. ACM201360534:134:4131246831281.68130 – reference: Kasteleyn, P. W.: Graph Theory and Crystal Physics. In: Harary, F. (ed.) Graph Theory and Theoretical Physics, pp 43–110. Academic Press, London (1967) – reference: ValiantLGQuantum circuits that can be simulated classically in polynomial timeSIAM J. Comput.200231412291254191996410.1137/S0097539700377025 – reference: Cai, J. Y., Lu, P., Xia, M.: Holographic algorithms by Fibonacci gates and holographic reductions for hardness. In: FOCS ’08: Proceedings of the 49th Annual IEEE Symposium on Foundations of Computer Science. IEEE Computer Society, Washington (2008) – reference: TemperleyHNVFisherMEDimer problem in statistical mechanics c an exact resultPhilos. Mag.196161061 C 106313639810.1080/14786436108243366 – reference: BulatovAADyerMEGoldbergLAJalseniusMJerrumMRicherbyDThe complexity of weighted and unweighted #CSPJ. Comput. Syst. Sci.2012782681688288135610.1016/j.jcss.2011.12.002 – reference: Cai, J., Lu, P., Xia, M.: Dichotomy for Holant* problems with domain size 3. In: Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2013, pp. 1278–1295, New Orleans (2013) – reference: IsingEBeitrag zur theorie des ferromagnetismusZ. Phys. Hadrons Nucl.19253112532581439.82056 – reference: LiebESokalAA general Lee-Yang theorem for one-component and multicomponent ferromagnetsCommun. Math. Phys.198180215317962315610.1007/BF01213009 – reference: BaxterRJExactly solved models in statistical mechanics1982LondonAcademic Press0538.60093 – reference: Schaefer, T. J.: The complexity of satisfiability problems. In: Proceedings of the 10th Annual ACM Symposium on Theory of Computing, pp. 216–226, San Diego (1978) – reference: YangCLeeTStatistical theory of equations of state and phase transitions. I. Theory of condensationPhys. Rev.19528734044095302810.1103/PhysRev.87.404 – reference: Backens, M.: A New Holant Dichotomy Inspired by Quantum Computation. In: 44Th International Colloquium on Automata, Languages, and Programming, ICALP 2017, Warsaw, pp. 16:1–16:14 (2017) – reference: HellPNešetřilJOn the complexity of H-coloringJ. Combin. Theory Ser. B199048192110104755510.1016/0095-8956(90)90132-J – reference: Cai, J. Y., Govorov, A.: Perfect matchings, rank of connection tensors and graph homomorphisms. In: Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA ’19, pp. 476–495. Society for Industrial and Applied Mathematics, Philadelphia (2019) – reference: YangCThe spontaneous magnetization of a two-dimensional Ising modelPhys. Rev.19528558088165174010.1103/PhysRev.85.808 – reference: Backens, M.: A Complete Dichotomy for Complex-Valued Holantc. In: 45Th International Colloquium on Automata, Languages, and Programming, ICALP 2018, pp. 12:1–12:14 (2018) – reference: LadnerREOn the structure of polynomial time reducibilityJ. ACM197522115517146469810.1145/321864.321877 – reference: ValiantLGHolographic algorithmsSIAM J. Comput.200837515651594238628110.1137/070682575https://doi.org/10.1137/070682575 – reference: Welsh, D.: Complexity: knots, colourings and counting. Cambridge University Press, Cambridge (1993) – reference: GoldbergLAGroheMJerrumMThurleyMA complexity dichotomy for partition functions with mixed signsSIAM J. Comput.201039733363402267807710.1137/090757496 – reference: LovászLOperations with structuresActa Math. Hung.19671832132821452910.1007/BF02280291 – reference: FreedmanMLovászLSchrijverAReflection positivity, rank connectivity, and homomorphism of graphsJ. AMS200720375122573961107.05089 – reference: SzegedyBEdge coloring models and reflection positivityJ. Amer. Math. Soc.200720969988232871210.1090/S0894-0347-07-00568-1 – reference: Cai, J., Lu, P., Xia, M.: Dichotomy for real Holantc problems. In: Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018, pp. 1802–1821, New Orleans (2018) – reference: Cai, J., Guo, H., Williams, T.: The Complexity of Counting Edge Colorings and a Dichotomy for Some Higher Domain Holant Problems. In: 55Th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2014, pp. 601–610, Philadelphia (2014) – reference: LeeTYangCStatistical theory of equations of state and phase transitions. II. Lattice gas and Ising modelPhys. Rev.19528734104195302910.1103/PhysRev.87.410 – reference: BulatovAAGroheMThe complexity of partition functionsTheor. Comput. Sci.20053482-3148186218137410.1016/j.tcs.2005.09.011 – reference: DyerMEGreenhillCSThe complexity of counting graph homomorphisms. Random StructAlgorithms2000173-426028918011350965.68073 – reference: Cai, J. Y., Lu, P., Xia, M.: Holant Problems and Counting CSP. In: Mitzenmacher, M. (ed.) STOC, pp 715–724. ACM (2009) – volume: 59 start-page: 25:1 issue: 5 year: 2012 ident: 9983_CR28 publication-title: J. ACM doi: 10.1145/2371656.2371660 – volume: 27 start-page: 1209 year: 1961 ident: 9983_CR33 publication-title: Physica doi: 10.1016/0031-8914(61)90063-5 – ident: 9983_CR20 – volume: 17 start-page: 260 issue: 3-4 year: 2000 ident: 9983_CR24 publication-title: Algorithms – ident: 9983_CR43 – ident: 9983_CR2 – ident: 9983_CR41 doi: 10.4159/harvard.9780674180758 – ident: 9983_CR8 doi: 10.1017/9781107477063 – volume: 87 start-page: 410 issue: 3 year: 1952 ident: 9983_CR36 publication-title: Phys. Rev. doi: 10.1103/PhysRev.87.410 – ident: 9983_CR15 doi: 10.1137/1.9781611975482.30 – volume: 38 start-page: 1970 issue: 5 year: 2009 ident: 9983_CR21 publication-title: SIAM J. Comput. doi: 10.1137/070690201 – ident: 9983_CR34 – ident: 9983_CR10 doi: 10.1109/FOCS.2014.70 – volume: 77 start-page: 41 issue: 1 year: 2011 ident: 9983_CR11 publication-title: J. Comput. Syst. Sci. doi: 10.1016/j.jcss.2010.06.005 – volume: 18 start-page: 321 year: 1967 ident: 9983_CR39 publication-title: Acta Math. Hung. doi: 10.1007/BF02280291 – volume: 60 start-page: 34:1 issue: 5 year: 2013 ident: 9983_CR4 publication-title: J. ACM – volume: 22 start-page: 155 issue: 1 year: 1975 ident: 9983_CR35 publication-title: J. ACM doi: 10.1145/321864.321877 – volume: 42 start-page: 924 issue: 3 year: 2013 ident: 9983_CR9 publication-title: SIAM J. Comput. doi: 10.1137/110840194 – ident: 9983_CR25 doi: 10.1145/1806689.1806789 – volume: 31 start-page: 253 issue: 1 year: 1925 ident: 9983_CR30 publication-title: Z. Phys. Hadrons Nucl. – ident: 9983_CR1 – volume: 22 start-page: 1087 issue: 5 year: 1993 ident: 9983_CR31 publication-title: SIAM J. Comput. doi: 10.1137/0222066 – ident: 9983_CR16 doi: 10.1109/FOCS.2008.34 – ident: 9983_CR48 doi: 10.1109/FOCS.2006.7 – volume: 37 start-page: 1565 issue: 5 year: 2008 ident: 9983_CR49 publication-title: SIAM J. Comput. doi: 10.1137/070682575 – volume: 65 start-page: 117 issue: 3-4 year: 1944 ident: 9983_CR42 publication-title: Phys. Rev. doi: 10.1103/PhysRev.65.117 – volume: 6 start-page: 1061 C 1063 year: 1961 ident: 9983_CR46 publication-title: Philos. Mag. doi: 10.1080/14786436108243366 – ident: 9983_CR14 doi: 10.1137/1.9781611975031.118 – ident: 9983_CR12 doi: 10.1137/1.9781611973082.132 – ident: 9983_CR44 doi: 10.1145/800133.804350 – volume: 80 start-page: 153 issue: 2 year: 1981 ident: 9983_CR37 publication-title: Commun. Math. Phys. doi: 10.1007/BF01213009 – ident: 9983_CR50 doi: 10.1017/CBO9780511752506 – volume: 39 start-page: 3336 issue: 7 year: 2010 ident: 9983_CR27 publication-title: SIAM J. Comput. doi: 10.1137/090757496 – ident: 9983_CR32 – volume: 87 start-page: 404 issue: 3 year: 1952 ident: 9983_CR52 publication-title: Phys. Rev. doi: 10.1103/PhysRev.87.404 – ident: 9983_CR7 doi: 10.1109/FOCS.2010.49 – volume: 20 start-page: 37 year: 2007 ident: 9983_CR26 publication-title: J. AMS – volume: 12 start-page: 581 issue: 2 year: 2002 ident: 9983_CR40 publication-title: Ann. Appl. Probab. doi: 10.1214/aoap/1026915617 – ident: 9983_CR17 doi: 10.1145/1536414.1536511 – ident: 9983_CR38 – ident: 9983_CR13 doi: 10.1137/1.9781611973105.93 – volume: 125 start-page: 1 issue: 1 year: 1996 ident: 9983_CR18 publication-title: Inf. Comput. doi: 10.1006/inco.1996.0016 – ident: 9983_CR19 doi: 10.1137/1.9780898718546 – volume: 78 start-page: 681 issue: 2 year: 2012 ident: 9983_CR5 publication-title: J. Comput. Syst. Sci. doi: 10.1016/j.jcss.2011.12.002 – volume: 348 start-page: 148 issue: 2-3 year: 2005 ident: 9983_CR6 publication-title: Theor. Comput. Sci. doi: 10.1016/j.tcs.2005.09.011 – volume-title: Exactly solved models in statistical mechanics year: 1982 ident: 9983_CR3 – volume: 76 start-page: 267 issue: 3-4 year: 2010 ident: 9983_CR22 publication-title: J. Comput. Syst. Sci. doi: 10.1016/j.jcss.2009.08.003 – volume: 31 start-page: 1229 issue: 4 year: 2002 ident: 9983_CR47 publication-title: SIAM J. Comput. doi: 10.1137/S0097539700377025 – volume: 85 start-page: 808 issue: 5 year: 1952 ident: 9983_CR51 publication-title: Phys. Rev. doi: 10.1103/PhysRev.85.808 – ident: 9983_CR23 doi: 10.1145/1314690.1314691 – volume: 48 start-page: 92 issue: 1 year: 1990 ident: 9983_CR29 publication-title: J. Combin. Theory Ser. B doi: 10.1016/0095-8956(90)90132-J – volume: 20 start-page: 969 year: 2007 ident: 9983_CR45 publication-title: J. Amer. Math. Soc. doi: 10.1090/S0894-0347-07-00568-1 |
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