On complexity analysis by quasi-interpretation

We present a survey on a method to analyse the program time and space complexity, based on termination orderings and quasi-interpretation. This method can be implemented to certify the runtime (or space) of programs. We demonstrate that the class of functions computed by first order functional programs over free algebras which terminate by permutation Path Ordering (resp. Lexicographic Path Ordering) and admit a quasi-interpretation bounded by a polynomial, is exactly the class of functions computable in polynomial time (resp. space).

[1]  Stephen A. Cook,et al.  Characterizations of Pushdown Machines in Terms of Time-Bounded Computers , 1971, J. ACM.

[2]  Nachum Dershowitz,et al.  Orderings for term-rewriting systems , 1979, 20th Annual Symposium on Foundations of Computer Science (sfcs 1979).

[3]  Nachum Dershowitz Orderings for Term-Rewriting Systems , 1979, FOCS.

[4]  Paliath Narendran,et al.  On Recursive Path Ordering , 1985, Theor. Comput. Sci..

[5]  Pierre Lescanne,et al.  Termination of Rewriting Systems by Polynomial Interpretations and Its Implementation , 1987, Sci. Comput. Program..

[6]  Robin Milner,et al.  Handbook of Theoretical Computer Science (Vol. B) , 1990 .

[7]  Dieter Hofbauer Termination Proofs by Multiset Path Orderings Imply Primitive Recursive Derivation Lengths , 1992, Theor. Comput. Sci..

[8]  Stephen A. Cook,et al.  A new recursion-theoretic characterization of the polytime functions (extended abstract) , 1992, STOC '92.

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

[10]  Neil D. Jones,et al.  Generalizing Cook's Transformation to Imperative Stack Programs , 1994, Results and Trends in Theoretical Computer Science.

[11]  Géraud Sénizergues Some Undecidable Termination Problems for Semi-Thue Systems , 1995, Theor. Comput. Sci..

[12]  J. Urgen Giesl Generating Polynomial Orderings for Termination Proofs ? , 1995 .

[13]  Andreas Weiermann,et al.  Termination Proofs for Term Rewriting Systems by Lexicographic Path Orderings Imply Multiply Recursive Derivation Lengths , 1995, Theor. Comput. Sci..

[14]  Yuri Gurevich,et al.  Tailoring Recursion for Complexity , 1995, J. Symb. Log..

[15]  Guillaume Bonfante,et al.  Complexity Classes and Rewrite Systems with Polynomial Interpretation , 1998, CSL.

[16]  Efficient First Order Functional Program Interpreter with Time Bound Certifications , 2000, LPAR.

[17]  M. Hofmann A Type System for Bounded Space and Functional In-Place Update , 2000, Nord. J. Comput..

[18]  Guillaume Bonfante,et al.  Constructions d'ordres, analyse de la complexité , 2000 .

[19]  Jean-Yves Moyen System Presentation: An Analyser of Rewriting Systems Complexity , 2001, Electron. Notes Theor. Comput. Sci..

[20]  Guillaume Bonfante,et al.  On Lexicographic Termination Ordering with Space Bound Certifications , 2001, Ershov Memorial Conference.

[21]  Roberto M. Amadio,et al.  Max-Plus Quasi-interpretations , 2003, TLCA.

[22]  Jean-Yves Marion,et al.  Analysing the implicit complexity of programs , 2003, Inf. Comput..

[23]  Silvano Dal-Zilio,et al.  A Functional Scenario for Bytecode Verification of Resource Bounds , 2004, CSL.