{"query": "The P versus NP chain - from the machine and the circuit to", "count": 20, "results": [{"id": "card_theory_computational_complexity__p__np__reductions", "title": "Computational complexity (P, NP, reductions)", "shelf": "theories", "surface": "secular", "snippet": "Computational complexity (P, NP, reductions) — an engine domain that can touch it: computer_science. Calibration: map-only — P vs NP is open, and this card says so. Not whether a problem can be solved", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_floor_millennium", "title": "The Millennium floor - seven open questions, and where they connect", "shelf": "codex", "surface": "secular", "snippet": "The seven Millennium Prize Problems on the one map of reality. 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D. Mulmuley 2011 — On P vs. NP and geometric complexity theory", "shelf": "millennium", "surface": "secular", "snippet": "K. D. Mulmuley (2011). On P vs. NP and geometric complexity theory. J. ACM 58 (2011) 5:1–26. DOI 10.1145/1944345.1944346. arXiv: 0908.1936. Canonical: https://doi.org/10.1145/1944345.1944346. Free cop", "authority_tier": "reference", "source": "K. D. Mulmuley (2011), J. ACM 58 (2011) 5:1–26", "readable": false, "generated": false}, {"id": "card_src_mill_deligne_1974", "title": "P. Deligne 1974 — La conjecture de Weil. I", "shelf": "millennium", "surface": "secular", "snippet": "P. Deligne (1974). La conjecture de Weil. I. Publ. Math. IHÉS 43 (1974) 273–307. DOI 10.1007/BF02684373. Canonical: https://doi.org/10.1007/BF02684373. Free copy: http://www.numdam.org/item/PMIHES_197", "authority_tier": "reference", "source": "P. Deligne (1974), Publ. Math. IHÉS 43 (1974) 273–307", "readable": false, "generated": false}, {"id": "card_src_mill_davis_matiyasevich_robinson_1976", "title": "M. Davis 1976 — Hilbert's tenth problem: Diophantine equations: positive aspects of a negative solution", "shelf": "millennium", "surface": "secular", "snippet": "M. Davis, Yu. Matiyasevich, J. Robinson (1976). Hilbert's tenth problem: Diophantine equations: positive aspects of a negative solution. Proc. Symp. Pure Math. 28 (AMS, 1976) 323–378. DOI 10.1090/pspu", "authority_tier": "reference", "source": "M. Davis, Yu. Matiyasevich, J. Robinson (1976), Proc. Symp. Pure Math. 28 (AMS, 1976) 323–378", "readable": false, "generated": false}, {"id": "card_src_mill_mulmuley_sohoni_2001", "title": "K. D. Mulmuley 2001 — Geometric complexity theory I: an approach to the P vs. NP and related problems", "shelf": "millennium", "surface": "secular", "snippet": "K. D. Mulmuley, M. Sohoni (2001). Geometric complexity theory I: an approach to the P vs. NP and related problems. SIAM J. Comput. 31 (2001) 496–526. DOI 10.1137/S009753970038715X. Canonical: https://", "authority_tier": "reference", "source": "K. D. Mulmuley, M. Sohoni (2001), SIAM J. Comput. 31 (2001) 496–526", "readable": false, "generated": false}, {"id": "card_floor_p_vs_np", "title": "The P versus NP chain - from the machine and the circuit to the three barriers", "shelf": "codex", "surface": "secular", "snippet": "Two trees. Computability: Turing's machine (1936), time as a resource (Hartmanis-Stearns 1965), feasible as polynomial in the input's length (Cobham 1965, Edmonds 1965). Circuits: Shannon's count of g", "authority_tier": "engine_derived", "source": "Narrow Highway - a chain on the one map (operator seed)", "readable": false, "generated": false}, {"id": "card_src_mill_manin_1971", "title": "Yu. I. Manin 1971 — Cyclotomic fields and modular curves", "shelf": "millennium", "surface": "secular", "snippet": "Yu. I. Manin (1971). Cyclotomic fields and modular curves. Russian Math. Surveys 26:6 (1971) 7–78. DOI 10.1070/RM1971v026n06ABEH001272. Canonical: https://doi.org/10.1070/RM1971v026n06ABEH001272. No f", "authority_tier": "reference", "source": "Yu. I. Manin (1971), Russian Math. Surveys 26:6 (1971) 7–78", "readable": false, "generated": false}, {"id": "card_question_p_vs_np", "title": "P versus NP", "shelf": "millennium", "surface": "secular", "snippet": "P versus NP. Is every problem whose solution can be checked in polynomial time also solvable in polynomial time? Its chart is the tick stick stick_p_versus_np: what is sealed, what is cited and what s", "authority_tier": "reference", "source": "Clay Mathematics Institute, the Millennium Prize Problems (2000)", "readable": false, "generated": false}, {"id": "card_src_mill_fghk_2016", "title": "M. G. Find 2016 — A better-than-3n lower bound for the circuit complexity of an explicit function", "shelf": "millennium", "surface": "secular", "snippet": "M. G. Find, A. Golovnev, E. A. Hirsch, A. S. Kulikov (2016). A better-than-3n lower bound for the circuit complexity of an explicit function. Proc. 57th IEEE FOCS (2016) 89–98; ECCC TR15-166 (2015, re", "authority_tier": "reference", "source": "M. G. Find, A. Golovnev, E. A. Hirsch, A. S. Kulikov (2016), Proc. 57th IEEE FOCS (2016) 89–98; ECCC TR15-166 (2015, revised 2022 as 'Improving 3n circuit complexity lower bounds')", "readable": false, "generated": false}, {"id": "card_src_mill_aaronson_2016", "title": "S. Aaronson 2016 — P =? NP", "shelf": "millennium", "surface": "secular", "snippet": "S. Aaronson (2016). P =? NP. Open Problems in Mathematics (Springer, 2016) 1–122. DOI 10.1007/978-3-319-32162-2_1. Canonical: https://doi.org/10.1007/978-3-319-32162-2_1. Free copy: https://www.scotta", "authority_tier": "reference", "source": "S. Aaronson (2016), Open Problems in Mathematics (Springer, 2016) 1–122", "readable": false, "generated": false}, {"id": "card_src_mill_williams_2011", "title": "R. Williams 2014 — Nonuniform ACC circuit lower bounds", "shelf": "millennium", "surface": "secular", "snippet": "R. Williams (2014). Nonuniform ACC circuit lower bounds. J. ACM 61 (2014) 2:1–32 (conference version CCC 2011). DOI 10.1145/2559903. Canonical: https://doi.org/10.1145/2559903. Free copy: https://peop", "authority_tier": "reference", "source": "R. Williams (2014), J. ACM 61 (2014) 2:1–32 (conference version CCC 2011)", "readable": false, "generated": false}, {"id": "card_src_mill_karp_1972", "title": "R. M. Karp 1972 — Reducibility among combinatorial problems", "shelf": "millennium", "surface": "secular", "snippet": "R. M. Karp (1972). Reducibility among combinatorial problems. Complexity of Computer Computations (Plenum, 1972) 85–103. DOI 10.1007/978-1-4684-2001-2_9. Canonical: https://doi.org/10.1007/978-1-4684-", "authority_tier": "reference", "source": "R. M. Karp (1972), Complexity of Computer Computations (Plenum, 1972) 85–103", "readable": false, "generated": false}, {"id": "card_src_mill_cook_1971", "title": "S. A. Cook 1971 — The complexity of theorem-proving procedures", "shelf": "millennium", "surface": "secular", "snippet": "S. A. Cook (1971). The complexity of theorem-proving procedures. Proc. 3rd ACM STOC (1971) 151–158. DOI 10.1145/800157.805047. Canonical: https://doi.org/10.1145/800157.805047. Free copy: https://www.", "authority_tier": "reference", "source": "S. A. Cook (1971), Proc. 3rd ACM STOC (1971) 151–158", "readable": false, "generated": false}, {"id": "card_src_mill_davis_logemann_loveland_1962", "title": "M. Davis 1962 — A machine program for theorem-proving", "shelf": "millennium", "surface": "secular", "snippet": "M. Davis, G. Logemann, D. Loveland (1962). A machine program for theorem-proving. Comm. ACM 5 (1962) 394–397. DOI 10.1145/368273.368557. Canonical: https://doi.org/10.1145/368273.368557. No free copy ", "authority_tier": "reference", "source": "M. Davis, G. Logemann, D. Loveland (1962), Comm. ACM 5 (1962) 394–397", "readable": false, "generated": false}, {"id": "card_src_mill_marques_silva_sakallah_1999", "title": "J. P. Marques-Silva 1999 — GRASP: a search algorithm for propositional satisfiability", "shelf": "millennium", "surface": "secular", "snippet": "J. P. Marques-Silva, K. A. Sakallah (1999). GRASP: a search algorithm for propositional satisfiability. IEEE Trans. Comput. 48 (1999) 506–521. DOI 10.1109/12.769433. Canonical: https://doi.org/10.1109", "authority_tier": "reference", "source": "J. P. Marques-Silva, K. A. Sakallah (1999), IEEE Trans. Comput. 48 (1999) 506–521", "readable": false, "generated": false}, {"id": "card_src_mill_blum_1984", "title": "N. Blum 1984 — A Boolean function requiring 3n network size", "shelf": "millennium", "surface": "secular", "snippet": "N. Blum (1984). A Boolean function requiring 3n network size. Theoret. Comput. Sci. 28 (1984) 337–345. DOI 10.1016/0304-3975(83)90029-4. Canonical: https://doi.org/10.1016/0304-3975(83)90029-4. Free c", "authority_tier": "reference", "source": "N. Blum (1984), Theoret. Comput. Sci. 28 (1984) 337–345", "readable": false, "generated": false}, {"id": "card_src_nuclide_np_219", "title": "Np-219 — np-219", "shelf": "nuclear_physics", "surface": "secular", "snippet": "Nuclide Np-219: 93 protons, 126 neutrons, mass number A=219. Half-life 0.00015 s. Primary decay: A 1%. Atomic mass 219.031602 u.", "authority_tier": "reference", "source": "NNDC / AME nuclide data (public domain)", "readable": false, "generated": false}], "house": {"door": "FIND", "kind": "cards", "trail": "results", "seal": null, "next_step": {"do": "open the top card", "door": "FIND", "tool": "card_get", "params": {"id": "card_theory_computational_complexity__p__np__reductions"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}