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(*   Copyright Dominique Larchey-Wendling [*]                 *)
(*             Yannick Forster            [+]                 *)
(*                                                            *)
(*                             [*] Affiliation LORIA -- CNRS  *)
(*                             [+] Affiliation Saarland Univ. *)
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(*      This file is distributed under the terms of the       *)
(*         CeCILL v2 FREE SOFTWARE LICENSE AGREEMENT          *)
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(** * List of all results *)
(** Reduction results for the following problems:  0) PCP: Post Correspondence Problem 1) BPCP: Binary Post Correspondence Problem (see Definitions.v) 2) BSM_HALTING: given a Binary Stack Machine P and an initial state st, starting at the first instruction of P with st as initial value for stacks, does the computation halt ? (see Bsm/bsm_defs.v) 3) MM_HALTING: given a Minsky Machine P starting at instruction 1, and an initial state v (the initial values of registers), does the computation starting from (1,v) reach the state (0,vec_zero) ? (see Mm/mm_defs.v) 4) EILL_PROVABILITY: given an EILL sequent (elementary fragment of ILL) is it provable in G_EILL ? (see Ll/eill.v) 5) ILL_PROVABILITY: given a sequent of the (!,&,-o) fragment of ILL is it provable in G_ILL ? (see Ll/ill.v) *)
Check PCP_BPCP.                           Print Assumptions PCP_BPCP.
Check BPCP_iBPCP.                         Print Assumptions BPCP_iBPCP.
Check iBPCP_BSM_HALTING.                  Print Assumptions iBPCP_BSM_HALTING.
Check BSM_MM_HALTING.                     Print Assumptions BSM_MM_HALTING.
Check BSM_MM_HALTS_ON_ZERO.               Print Assumptions BSM_MM_HALTS_ON_ZERO.
Check MM_HALTS_ON_ZERO_EILL_PROVABILITY.  Print Assumptions MM_HALTS_ON_ZERO_EILL_PROVABILITY.
Check EILL_ILL_PROVABILITY.               Print Assumptions EILL_ILL_PROVABILITY.

(* Specifications: *)
Theorem PCP_BSM_HALTING : PCP ⪯ BSM_HALTING.
Theorem PCP_MM_HALTS_ON_ZERO : PCP ⪯ MM_HALTS_ON_ZERO.
Theorem PCP_MM_HALTING : PCP ⪯ MM_HALTING.
Theorem PCP_ILL : PCP ⪯ ILL_PROVABILITY.
Module Def_of_undec.