Theoretical Computer Science
Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
Termination proofs by multiset path orderings imply primitive recursive derivation lengths
Theoretical Computer Science - Selected papers of the Second International Conference on algebraic and logic programming, Nancy, France, October 1–3, 1990
Hilbert's tenth problem
Computability and complexity: from a programming perspective
Computability and complexity: from a programming perspective
Term rewriting and all that
Termination of term rewriting using dependency pairs
Theoretical Computer Science - Trees in algebra and programming
Term Rewriting Systems
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
On Lexicographic Termination Ordering with Space Bound Certifications
PSI '02 Revised Papers from the 4th International Andrei Ershov Memorial Conference on Perspectives of System Informatics: Akademgorodok, Novosibirsk, Russia
Termination Proofs and the Length of Derivations (Preliminary Version)
RTA '89 Proceedings of the 3rd International Conference on Rewriting Techniques and Applications
Polynomial Interpretations and the Complexity of Algorithms
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
Algorithms with polynomial interpretation termination proof
Journal of Functional Programming
Applicable Algebra in Engineering, Communication and Computing
Mechanically Proving Termination Using Polynomial Interpretations
Journal of Automated Reasoning
Practical use of polynomials over the reals in proofs of termination
Proceedings of the 9th ACM SIGPLAN international conference on Principles and practice of declarative programming
Matrix Interpretations for Proving Termination of Term Rewriting
Journal of Automated Reasoning
Characterizations of polynomial complexity classes with a better intensionality
Proceedings of the 10th international ACM SIGPLAN conference on Principles and practice of declarative programming
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
Proving Quadratic Derivational Complexities Using Context Dependent Interpretations
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
Automated Implicit Computational Complexity Analysis (System Description)
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Automated Complexity Analysis Based on the Dependency Pair Method
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Sup-interpretations, a semantic method for static analysis of program resources
ACM Transactions on Computational Logic (TOCL)
Efficient first order functional program interpreter with time bound certifications
LPAR'00 Proceedings of the 7th international conference on Logic for programming and automated reasoning
SAT solving for termination analysis with polynomial interpretations
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
Quasi-interpretation synthesis by decomposition an application to higher-order programs
ICTAC'07 Proceedings of the 4th international conference on Theoretical aspects of computing
Revisiting matrix interpretations for polynomial derivational complexity of term rewriting
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
Quasi-interpretations a way to control resources
Theoretical Computer Science
Joint spectral radius theory for automated complexity analysis of rewrite systems
CAI'11 Proceedings of the 4th international conference on Algebraic informatics
SAT Modulo Linear Arithmetic for Solving Polynomial Constraints
Journal of Automated Reasoning
Complexity invariance of real interpretations
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Quasi-interpretations and small space bounds
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
Synthesis of max-plus quasi-interpretations
Fundamenta Informaticae - Typed Lambda Calculi and Applications 2003, Selected Papers
Hi-index | 5.23 |
In this paper, we survey the complexity of distinct methods that allow the programmer to synthesize a sup-interpretation, a function providing an upper-bound on the size of the output values computed by a program. It consists in a static space analysis tool without consideration of the time consumption. Although clearly related, sup-interpretation is independent from termination since it only provides an upper bound on the terminating computations. First, we study some undecidable properties of sup-interpretations from a theoretical point of view. Next, we fix term rewriting systems as our computational model and we show that a sup-interpretation can be obtained through the use of a well-known termination technique, the polynomial interpretations. The drawback is that such a method only applies to total functions (strongly normalizing programs). To overcome this problem we also study sup-interpretations through the notion of quasi-interpretation. Quasi-interpretations also suffer from a drawback that lies in the subterm property. This property drastically restricts the shape of the considered functions. Again we overcome this problem by introducing a new notion of interpretations mainly based on the dependency pairs method. We study the decidability and complexity of the sup-interpretation synthesis problem for all these three tools over sets of polynomials. Finally, we take benefit of some previous works on termination and runtime complexity to infer sup-interpretations.