Horn Linear Logic and Minsky Machines

Here we give a detailed proof for the crucial point in our Minsky machine simulation - that any linear logic derivation for a specific Horn sequent can be transformed into a Minsky computation leading from an initial configuration to the halting configuration. Among other things, the presentation advantage of the 3-step program is that the non-trivial tricky points are distributed between the independent parts each of which we justify following its own intrinsic methodology (to say nothing of the induction used in the opposite directions): (1) From LL to HLL - we use purely proof-theoretic arguments. (2) From HLL to Horn programs - we translate trees (HLL derivations) into another trees (Horn programs)of the same shape, almost. (3) From Horn programs to Minsky computations - we use purely computational arguments.

[1]  Max I. Kanovich,et al.  The Complexity of Horn Fragments of Linear Logic , 1994, Ann. Pure Appl. Log..

[2]  P. Lincoln Deciding provability of linear logic formulas , 1995 .

[3]  Narciso Martí-Oliet,et al.  From Petri nets to linear logic , 1989, Mathematical Structures in Computer Science.

[4]  Carl A. Gunter,et al.  Normal process representatives , 1990, [1990] Proceedings. Fifth Annual IEEE Symposium on Logic in Computer Science.

[5]  M. Minsky Recursive Unsolvability of Post's Problem of "Tag" and other Topics in Theory of Turing Machines , 1961 .

[6]  Jean-Yves Girard,et al.  Linear logic: its syntax and semantics , 1995 .

[7]  Max I. Kanovich The direct simulation of Minsky machines in linear logic , 1995 .

[8]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[9]  Max I. Kanovich Horn programming in linear logic is NP-complete , 1992, [1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science.

[10]  S. Rao Kosaraju,et al.  Decidability of reachability in vector addition systems (Preliminary Version) , 1982, STOC '82.

[11]  Ernst W. Mayr An Algorithm for the General Petri Net Reachability Problem , 1984, SIAM J. Comput..

[12]  Patrick Lincoln,et al.  Linear logic , 1992, SIGA.

[13]  Max I. Kanovich,et al.  Linear Logic as a Logic of Computations , 1994, Ann. Pure Appl. Log..

[14]  Max I. Kanovich,et al.  Petri Nets, Horn Programs, Linear Logic and Vector Games , 1995, Ann. Pure Appl. Log..