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On the Computational Content of Termination Proofs [chapter]

Georg Moser, Thomas Powell
2015 Lecture Notes in Computer Science  
We demonstrate that by analysing our realiser we are able to derive, in a completely uniform manner, a number of results on the relationship between the strength of path orders and the bounds they induce  ...  Given that a program has been shown to terminate using a particular proof, it is natural to ask what we can infer about its complexity.  ...  Is it possible to derive computational content from a given termination argument, so that we can automatically deduce bounds on the complexity of our programs ?  ... 
doi:10.1007/978-3-319-20028-6_28 fatcat:ca2wbwgtg5exlf6fdbuy57ow2m

A proof-theoretical investigation of Zantema's problem [chapter]

Thierry Coquand, Henrik Persson
1998 Lecture Notes in Computer Science  
We present a concrete example of how one can extract constructive content from a non{constructive proof. The proof investigated is a termination proof of the string{rewriting system 1100 ! 000111.  ...  This rewriting system is self{embedding, so the standard termination techniques which rely on Kruskal's Tree Theorem cannot be applied directly.  ...  Let us illustrate this point on the proof of Lemma 8: What is the computational content of a ! a 0 ) Acc ! (a 0 )? It should be a function g a of type B] !  ... 
doi:10.1007/bfb0028014 fatcat:wzefresu6rfahc45omf45gbeom

Code-carrying theory

Aytekin Vargun, David R. Musser
2008 Proceedings of the 2008 ACM symposium on Applied computing - SAC '08  
An Abstract of a Thesis Submitted to the Graduate  ...  (evolve Sum-list-theory [sum-list-compute-termination sum-list-compute-termination-proof]) • Consistency of sum-list-compute: In computing the consistency condition of sum-list-compute, the producer passes  ...  uspec* sum-list-compute-termination [L y])))) where we use the already established sum-list-compute-termination property in the proof of the inductive step.  ... 
doi:10.1145/1363686.1363780 dblp:conf/sac/VargunM08 fatcat:4v52prelxnhmzjk5quc4ggzqde

Unifying stabilization and termination in message-passing systems

Anish Arora, Mikhail Nesterenko
2005 Distributed computing  
We consider a rather general notion of termination: a terminating program eventually stops its execution after the environment ceases to provide input.  ...  On the flip side, they show that other problems such as mutual exclusion and reliable-transmission allow such solutions.  ...  On the basis of this proof we show that the consensus problem is not termination-symmetric and thus does not admit a stabilizing and terminating solution.  ... 
doi:10.1007/s00446-004-0111-6 fatcat:av465objfngxnknwugj5vengp4

Page 5241 of Mathematical Reviews Vol. , Issue 98H [page]

1998 Mathematical Reviews  
Christoph Lith, Compositional term rewriting: an algebraic proof of Toyama’s theorem (261-275); Ralf Treinen, The first- order theory of one-step rewriting 1s undecidable (276-286); Man- fred Schmidt-SchauB  ...  Festschrift in honor of Michael Gelfond. Proceedings of the symposium held in honor of Michael Gelfond on his 50th birthday in El Paso, TX, November 5, 1995.  ... 

Page 9235 of Mathematical Reviews Vol. , Issue 2001M [page]

2001 Mathematical Reviews  
This system thus completely ‘dissolves’ the syntax of the formulas and retains only their behavioural content as far as proof construction is concerned.  ...  One of the base- lines of the paper is to avoid relying on syntax to describe the key mechanisms of the paradigm.  ... 

On the Computational Power of Brane Calculi [chapter]

Nadia Busi, Roberto Gorrieri
2006 Lecture Notes in Computer Science  
On the other hand, we show the impossibility to define a "faithful" encoding of Random Access Machines in the Mate/Bud/Drip calculus, by providing a proof of the decidability of the existence of a divergent  ...  In this paper we investigate and compare the expressiveness of such two calculi w.r.t. their ability to act as computational devices.  ...  Acknowledgement: We thank the anonymous referees for their comments. We are indebted to Fabien Tarissan for his careful comments and precious suggestions.  ... 
doi:10.1007/11880646_2 fatcat:5s3zk5oi3bazpcpeok6zk4e3hi

But What if I Don't Want to Wait Forever?

Colin Fidge, Carron Shankland
2003 Formal Aspects of Computing  
By formal reasoning based on this description, we establish the probability of the root contention part of the protocol successfully terminating in terms of the number of attempts to do so.  ...  Some simple calculations then allow us to establish an upper bound on the time taken for those attempts.  ...  the Carnegie Trust for the Universities of Scotland.  ... 
doi:10.1007/s001650300006 fatcat:ool2iauerva5bdodwznayargg4

On the expressive power of recursion, replication and iteration in process calculi

2009 Mathematical Structures in Computer Science  
These results are obtained by considering the decidability of four basic properties: termination (i.e. all computations are finite), convergence (i.e. the existence of a finite computation), barb (i.e.  ...  We investigate the expressive power of three alternative approaches for the definition of infinite behaviors in process calculi, namely, recursive definitions, replication and iteration.  ...  Acknowledgments -We thank Lucia Acciai for pointing out an error in a preliminary version of the paper, and the anonymous referees for their comments useful to improve the presentation.  ... 
doi:10.1017/s096012950999017x fatcat:eig4d6er6ndebodb4shkkrkhiy

Contents and Index of Volume 34

2002 Journal of symbolic computation  
, V., Comparing Approaches to the Exploration of the Domain of Residue Classes, 287 Modular Termination Proofs for Rewriting Using Dependency Pairs, 21 Monico, C., Computing the Primary Decomposition of  ...  119 Gaál, I., On the Resolution of Resultant Type Equations .  ... 
doi:10.1006/jsco.2002.0054 fatcat:inux3tyyf5hudciuedurgediii

Page 4309 of Mathematical Reviews Vol. , Issue 88h [page]

1988 Mathematical Reviews  
Contents: Introduction; Notations; 1. Proofs of programs: In- troduction; Proofs of partial correctness; proofs of termination; Analysis of iterative programs; 2.  ...  Proof and analysis of recursive programs: Introduction; Proofs of partial correctness of recursive procedures; Example; Proof of termination of a recursive procedure; Analysis of a recursive procedure;  ... 

Saturation-based theorem proving: Past successes and future potential [chapter]

Harald Ganzinger
1996 Lecture Notes in Computer Science  
combinations of theories p. 463 Ground resolution with group computations on semantic symmetries p. 478 A new method for knowledge compilation: the achievement by cycle search p. 493 Rewrite  ...  based on semi-lattices p. 688Grammar specification in categorial logics and theorem proving p. 703Table of Contents provided by Blackwell's Book Services and R.R.  ... 
doi:10.1007/3-540-61511-3_64 fatcat:iizfu32trnfadmj4z7xcvwds5y

The concurrency hierarchy, and algorithms for unbounded concurrency

Eli Gafni, Michael Merritt, Gadi Taubenfeld
2001 Proceedings of the twentieth annual ACM symposium on Principles of distributed computing - PODC '01  
We study walt-free computation using (read/write) shared memory under a range of assumptions on the arrival pattern of processes.  ...  Under the condition that no process takes infinitely many steps without terminating, for any finite bound k > 0, we show that bounding concurrency reveals a strict hierarchy of computational models: a  ...  The results of this section are essentially a corollary of the following impossibility result (the proof of which uses sophisticated topological characterization of asynchronous computability): Lemma  ... 
doi:10.1145/383962.384008 dblp:conf/podc/GafniMT01 fatcat:5g7poiutiffbnaqxjfq5wwpsha

Verifying lossy channel systems has nonprimitive recursive complexity

Ph. Schnoebelen
2002 Information Processing Letters  
Lossy channel systems are systems of finite state automata that communicate via unreliable unbounded fifo channels.  ...  It is known that reachability, termination and a few other verification problems are decidable for these systems.  ...  Acknowledgements We are grateful to Alain Finkel who brought this topic to our attention, to Petr Jančar who suggested major improvements on an earlier draft, and to the anonymous referee who helped us  ... 
doi:10.1016/s0020-0190(01)00337-4 fatcat:uclxhpqzgvc5thoklhlpihmpu4


Ulrich Berger, Monika Seisenberger
2005 From Sets and Types to Topology and Analysis  
We describe two methods of extracting constructive content from classical proofs, focusing on theorems involving infinite sequences and nonconstructive choice principles.  ...  in term rewriting theory for termination proofs [CTB94,Tou02].  ...  The meaning of ∀ nc x ρ A(x) is roughly 'A(x) has been established for all x with a proof whose computational content does not depend on x'.  ... 
doi:10.1093/acprof:oso/9780198566519.003.0008 fatcat:n4z453pujrenfgte7abt4tkjhi
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