An arithmetic for polynomial-time computation

We define a restriction LHA of Heyting arithmetic HA with the property that all extracted programs are feasible. The restrictions consist in linearity and ramification requirements.

[1]  Daniel Leivant,et al.  Lambda Calculus Characterizations of Poly-Time , 1993, Fundam. Informaticae.

[2]  Helmut Schwichtenberg,et al.  Feasible Computation with Higher Types , 2002 .

[3]  Klaus Aehlig,et al.  A syntactical analysis of non-size-increasing polynomial time computation , 2000, Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332).

[4]  Ulrich Berger,et al.  Program Extraction from Normalization Proofs , 2006, Stud Logica.

[5]  Ulrich Berger,et al.  Program Extraction from Normalization Proofs , 2006, Stud Logica.

[6]  S. Shelah,et al.  Annals of Pure and Applied Logic , 1991 .

[7]  Jean-Yves Girard.  Light Linear Logic , 1994, LCC.

[8]  Daniel Leivant,et al.  Intrinsic Theories and Computational Complexity , 1994, LCC.

[9]  Martin Hofmann,et al.  An arithmetic for non-size-increasing polynomial-time computation , 2004, Theor. Comput. Sci..

[10]  Frank Pfenning,et al.  Intensionality, extensionality, and proof irrelevance in modal type theory , 2001, Proceedings 16th Annual IEEE Symposium on Logic in Computer Science.

[11]  Andre Scedrov,et al.  Bounded Linear Logic , 1991 .

[12]  Daniel Leivant.  Termination Proofs and Complexity Certification , 2001, TACS.

[13]  Daniel Leivant,et al.  Ramified Recurrence and Computational Complexity IV : Predicative Functionals and Poly-Space , 2000 .

[14]  A. Troelstra.  Metamathematical investigation of intuitionistic arithmetic and analysis , 1973 .

[15]  Martin Hofmann,et al.  A New "Feasible" Arithmetic , 2002, J. Symb. Log..

[16]  D. Hilbert.  Über das Unendliche , 1926 .

[17]  Bruce M. Kapron,et al.  Characterizations of the basic feasible functionals of finite type , 1989, 30th Annual Symposium on Foundations of Computer Science.

[18]  Martin Hofmann,et al.  Linear types and non-size-increasing polynomial time computation , 1999, Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158).

[19]  Helmut Schwichtenberg,et al.  Higher type recursion, ramification and polynomial time , 2000, Ann. Pure Appl. Log..

[20]  Stanley S. Wainer,et al.  Elementary arithmetic , 2005, Ann. Pure Appl. Log..

[21]  Stephen A. Cook,et al.  A new recursion-theoretic characterization of the polytime functions , 1992, STOC '92.

[22]  Jean-Yves Marion.  Actual Arithmetic and Feasibility , 2001, CSL.

[23]  Von Kurt Gödel,et al.  ÜBER EINE BISHER NOCH NICHT BENÜTZTE ERWEITERUNG DES FINITEN STANDPUNKTES , 1958 .

[24]  Harold Simmons,et al.  The realm of primitive recursion , 1988, Arch. Math. Log..

[25]  Stephen A. Cook,et al.  Computability and Complexity of Higher Type Functions , 1992 .

[26]  Peter Clote,et al.  Bounded Arithmetic for NC, ALogTIME, L and NL , 1992, Ann. Pure Appl. Log..

[27]  Andre Scedrov,et al.  Bounded Linear Logic: A Modular Approach to Polynomial-Time Computability , 1992, Theor. Comput. Sci..

[28]  Jean-Pierre Bourguignon,et al.  Mathematische Annalen , 1893 .