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Automatically Proving and Disproving Feasibility Conditions [chapter]

Raúl Gutiérrez, Salvador Lucas
2020 Lecture Notes in Computer Science  
We introduce a framework for proving feasibility/infeasibility, and a new tool, infChecker, which implements it.  ...  In the realm of term rewriting, given terms s and t, a reachability condition s → * t is called feasible if there is a substitution σ such that σ(s) rewrites into σ(t) in zero or more steps; otherwise,  ...  We thank the anonymous referees for many remarks and suggestions that led to improve the paper.  ... 
doi:10.1007/978-3-030-51054-1_27 fatcat:fhetmi5dufd4fheewthjtpgqka

Convexity and Concavity Detection in Computational Graphs: Tree Walks for Convexity Assessment

Robert Fourer, Chandrakant Maheshwari, Arnold Neumaier, Dominique Orban, Hermann Schichl
2010 INFORMS journal on computing  
As a consequence, convexity of the feasible set may be assessed to some extent.  ...  In this paper, we examine sets of symbolic tools associated to modeling systems for mathematical programming which can be used to automatically detect the presence or lack of convexity and concavity in  ...  The column Ω gives the convexity of the feasible set and t is the running time in seconds for the convexity proving and disproving phases.  ... 
doi:10.1287/ijoc.1090.0321 fatcat:s77m4hew6vgljeon6p24tfzvve

Proving and disproving information inequalities

Siu-Wai Ho, Chee Wei Tan, Raymond W. Yeung
2014 2014 IEEE International Symposium on Information Theory  
When a given information inequality cannot be proved, the sufficient conditions for a counterexample to disprove the information inequality are found by linear programming.  ...  Under this framework, this paper considers a few other problems that can be solved by using Lagrange duality and convex approximation.  ...  (Dual feasibility) Hence, (11) follows because it is the stationarity of the Lagrangian in the KKT conditions. Then we can have the following direct consequence.  ... 
doi:10.1109/isit.2014.6875347 dblp:conf/isit/HoTY14 fatcat:emwo2bgqprg4vaidrbbjeggfeq

Proving Infinite Satisfiability [chapter]

Peter Baumgartner, Joshua Bax
2013 Lecture Notes in Computer Science  
Then disproving is done by proving that the negated conjecture follows.  ...  We consider the problem of automatically disproving invalid conjectures over data structures such as lists and arrays over integers, in the presence of additional hypotheses over these data structures.  ...  Introduction We consider the problem of automatically disproving invalid conjectures over data structures such as lists and arrays over integers, in the presence of additional hypotheses over these data  ... 
doi:10.1007/978-3-642-45221-5_6 fatcat:levblismuzfavjzugepndz2kmi

Page 6967 of Mathematical Reviews Vol. , Issue 95k [page]

1995 Mathematical Reviews  
We present procedures to test sufficient complete- ness and to prove and disprove inductive properties automatically in parameterized conditional specifications.  ...  Automat. Reason. 12 (1994), no. 3, 359-388. Summary: “Recently we proposed [S. J. Lee and D. A. Plaisted, J. Automat.  ... 

Termination of just/fair computations in term rewriting

Salvador Lucas, José Meseguer
2008 Information and Computation  
The main goal of this paper is to apply rewriting termination technology-enjoying a quite mature set of termination results and tools-to the problem of proving automatically the termination of concurrent  ...  Our theoretical results are combined into a practical proof method for proving fair-termination that can be automated and can be supported by current termination tools.  ...  However, by Proposition 11, termination of → * S • → R F (which we can try to prove automatically by the methods and tools discussed in Section 6.1) is a sufficient condition for termination of ( → S ∩  ... 
doi:10.1016/j.ic.2007.11.002 fatcat:4csdti3cmrgtdgstepigsrp5ye

Valigator: A Verification Tool with Bound and Invariant Generation [chapter]

Thomas A. Henzinger, Thibaud Hottelier, Laura Kovács
2008 Lecture Notes in Computer Science  
The system offers support for automatically generating and proving verification conditions and, most importantly, for automatically inferring loop invariants and bound assertions by means of symbolic summation  ...  , Gröbner basis computation, and quantifier elimination.  ...  uses the automated theorem proving tools Z3, CVC3, and STP [11, 5, 15] for proving the correctness of the verification conditions.  ... 
doi:10.1007/978-3-540-89439-1_24 fatcat:ldt6quupwrghpbwlnohwuln5rm

Supporting Global Numerical Optimization of Rational Functions by Generic Symbolic Convexity Tests [chapter]

Winfried Neun, Thomas Sturm, Stefan Vigerske
2010 Lecture Notes in Computer Science  
We propose to apply symbolic methods to prove or disprove convexity of rational functions over a polyhedral domain. Our algorithms reduce convexity questions to real quantifier elimination problems.  ...  Our methods are implemented and publicly available in the open source computer algebra system Reduce.  ...  In this paper, we present a novel symbolic method to prove or disprove convexity of rational functions over polyhedral sets.  ... 
doi:10.1007/978-3-642-15274-0_19 fatcat:mkkoqo2nfbfopf6iwnycjrskbu

Applications of feasible path analysis to program testing

Allen Goldberg, T. C. Wang, David Zimmerman
1994 Proceedings of the 1994 international symposium on Software testing and analysis - ISSTA '94  
This paper describes the design and prototype implementation of a structural testing system that uses a theorem prover to determine feasibility of testing requirements and to optimize * Work performed  ...  Acknowledgments: Part of this work has been supported by NASA and Boeing Corporation.  ...  prover is focused on disproving a non-theorem, instead of, as is usual, proving a theorem.  ... 
doi:10.1145/186258.186523 dblp:conf/issta/GoldbergWZ94 fatcat:q5sa4lqjbbfyrhaq6vwvflcsxm

Predicate Abstraction and CEGAR for Disproving Termination of Higher-Order Functional Programs [chapter]

Takuya Kuwahara, Ryosuke Sato, Hiroshi Unno, Naoki Kobayashi
2015 Lecture Notes in Computer Science  
We propose an automated method for disproving termination of higher-order functional programs. Our method combines higherorder model checking with predicate abstraction and CEGAR.  ...  Thus, disproving non-termination reduces to the problem of checking a certain branching property of the abstract program, which can be solved by higher-order model checking.  ...  Acknowledgments We would like to thank Carsten Fuhs for providing us with their experimental data and pointers to related work, and anonymous referees for useful comments.  ... 
doi:10.1007/978-3-319-21668-3_17 fatcat:bzmso4xxbrdgfdoj2uanvbjtfy

Formal Verification and Validation of ERTMS Industrial Railway Train Spacing System [chapter]

Alessandro Cimatti, Raffaele Corvino, Armando Lazzaro, Iman Narasamdya, Tiziana Rizzo, Marco Roveri, Angela Sanseviero, Andrei Tchaltsev
2012 Lecture Notes in Computer Science  
Moreover, the results of experiments show that formal verification and validation is feasible and effective, and also scales reasonably well with the size of the configuration.  ...  To show feasibility, effectiveness and scalability, we have experimented with several state of the art symbolic software model checking techniques and tools on different network configurations.  ...  Finally, for the certification of the application, as mandated by the standards, we will work on the certification and qualification of KRATOS and NUSMV.  ... 
doi:10.1007/978-3-642-31424-7_29 fatcat:rt4ps25dbfcrfeplvkry3z36i4

Page 7157 of Mathematical Reviews Vol. , Issue 89M [page]

1989 Mathematical Reviews  
V. (2-AOSUK-B) Solution of multicriterial variational problems under indeterminacy conditions. Soviet J. Automat. Inform.  ...  This index condition replaces common regularity conditions such as linear independence of the gradients or Slater’s condition, and it is simpler and less restrictive than the Property U used by the author  ... 

Replacing conjectures by positive knowledge: Inferring proven precise worst-case execution time bounds using symbolic execution

Jens Knoop, Laura Kovács, Jakob Zwirchmayr
2017 Journal of symbolic computation  
In this article we present an approach for inferring and proving WCET bounds precise. This approach guarantees that the WCET bound is computed for a feasible system trace.  ...  In this article we address this challenge and describe a rigorous approach for the timing analysis of programs and for proving its results precise.  ...  We acknowledge funding from the Vienna University of Technology, the Austrian research project FWF S11409-N23, the ERC Starting Grant 2014 SYMCAR 639270, the Wallenberg Academy Fellowship 2014, and the  ... 
doi:10.1016/j.jsc.2016.07.023 fatcat:q6ryk5iwdvhc3gi56zzo5hun2q

A Semantic Approach to the Analysis of Rewriting-Based Systems [article]

Salvador Lucas
2017 arXiv   pre-print
In this paper we show that a number of interesting properties of rewriting-based systems can be investigated in this way, including infeasibility and non-joinability of critical pairs in (conditional)  ...  Properties expressed as the provability of a first-order sentence can be disproved by just finding a model of the negation of the sentence.  ...  I thank María Alpuente and José Meseguer for fruitful discussions about the topics in this paper.  ... 
arXiv:1709.05095v1 fatcat:q4gcgjyxxzfbbcg5mkahpxkjge

mu-term: Verify Termination Properties Automatically (System Description) [chapter]

Raúl Gutiérrez, Salvador Lucas
2020 Lecture Notes in Computer Science  
We report on the new version of mu-term, a tool for proving termination properties of variants of rewrite systems, including conditional, context-sensitive, equational, and order-sorted rewrite systems  ...  The automatic generation of logical models for suitable firstorder theories and formulas provides a common basis to implement the proofs.  ...  We thank the anonymous referees for many remarks and suggestions that led to improve the paper.  ... 
doi:10.1007/978-3-030-51054-1_28 fatcat:hfw3ljwsajdm7nzubf4ok6s4de
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