On the Church-Rosser property for the direct sum of term rewriting systems
Journal of the ACM (JACM)
Counterexamples to termination for the direct sum of term rewriting systems
Information Processing Letters
Modularity of simple termination of term rewriting systems with shared constructors
Theoretical Computer Science
Handbook of logic in computer science (vol. 2)
Modular proofs for completeness of hierarchical term rewriting systems
Selected papers of the thirteenth conference on Foundations of software technology and theoretical computer science
Computability and complexity: from a programming perspective
Computability and complexity: from a programming perspective
Information and Computation
The strength of non-size increasing computation
POPL '02 Proceedings of the 29th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Advanced topics in term rewriting
Advanced topics in term rewriting
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
Generalized Sufficient Conditions for Modular Termination of Rewriting
Proceedings of the Third International Conference on Algebraic and Logic Programming
CTRS '94 Proceedings of the 4th International Workshop on Conditional and Typed Rewriting Systems
A type system for bounded space and functional in-place update
Nordic Journal of Computing
Definitional interpreters for higher-order programming languages
ACM '72 Proceedings of the ACM annual conference - Volume 2
Soft linear logic and polynomial time
Theoretical Computer Science - Implicit computational complexity
Certifying Polynomial Time and Linear/Polynomial Space for Imperative Programs
SIAM Journal on Computing
Principal Typing for Lambda Calculus in Elementary Affine Logic
Fundamenta Informaticae - Typed Lambda Calculi and Applications 2003, Selected Papers
Max-plus quasi-interpretations
TLCA'03 Proceedings of the 6th international conference on Typed lambda calculi and applications
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
Quasi-interpretations a way to control resources
Theoretical Computer Science
Resource bound certification for a tail-recursive virtual machine
APLAS'05 Proceedings of the Third Asian conference on Programming Languages and Systems
A feasible algorithm for typing in elementary affine logic
TLCA'05 Proceedings of the 7th international conference on Typed Lambda Calculi and Applications
The flow of data and the complexity of algorithms
CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms
Automated Implicit Computational Complexity Analysis (System Description)
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Cdiprover3: a tool for proving derivational complexities of term rewriting systems
ESSLLI'08/09 Proceedings of the 2008 international conference on Interfaces: explorations in logic, language and computation
POP and semantic labeling using SAT
ESSLLI'08/09 Proceedings of the 2008 international conference on Interfaces: explorations in logic, language and computation
Synthesis of sup-interpretations: A survey
Theoretical Computer Science
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Quasi-interpretation analysis belongs to the field of implicit computational complexity (ICC) and has shown its interest to deal with resource analysis of first-order functional programs, which are terminating or not. In this paper, we tackle the issue of program decomposition wrt quasi-interpretations analysis. For that purpose, we use the notion of modularity. Firstly, modularity decreases the complexity of the quasi-interpretation search algorithms. Secondly, modularity increases the intentionality of the quasi-interpretation method, that is the number of captured programs. Finally, we take advantage of modularity conditions to extend smoothly quasi-interpretations to higher-order programs. We study the modularity of quasi-interpretations through the notions of constructor-sharing and hierarchical unions of programs. We show that, in both cases, the existence of quasi-interpretations is no longer a modular property. However, we can still certify the complexity of programs by showing, under some restrictions, that the size of the values computed by a program remains polynomially bounded by the inputs size.