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Certifying Confluence of Quasi-Decreasing Strongly Deterministic Conditional Term Rewrite Systems [chapter]

Christian Sternagel, Thomas Sternagel
2017 Lecture Notes in Computer Science  
We formalize a confluence criterion for the class of quasidecreasing strongly deterministic conditional term rewrite systems in Isabelle/HOL: confluence follows if all conditional critical pairs are joinable  ...  However, quasi-decreasingness, strong determinism, and joinability of conditional critical pairs are all undecidable in general.  ...  We formalized a characterization of confluence of quasi-decreasing strongly deterministic CTRSs in Isabelle/HOL.  ... 
doi:10.1007/978-3-319-63046-5_26 fatcat:xfynwx3ddfbe5fo2ndsushokqq

Formalized Confluence of Quasi-Decreasing, Strongly Deterministic Conditional TRSs [article]

Thomas Sternagel, Christian Sternagel
2016 arXiv   pre-print
We present an Isabelle/HOL formalization of a characterization of confluence for quasi-reductive strongly deterministic conditional term rewrite systems, due to Avenhaus and Lor\'ia-S\'aenz.  ...  A strongly deterministic oriented 3-CTRS (SDTRS) R is a set of conditional rewrite rules of the shape ℓ → r ⇐ c where ℓ and r are terms and c is a possibly empty sequence of pairs of terms s 1 ≈ t 1 ,  ...  Introduction Already in 1994 Avenhaus and Loría-Sáenz [1] proved a critical pair criterion for deterministic conditional term rewrite systems with extra variables in right-hand sides, provided their  ... 
arXiv:1609.03341v1 fatcat:jyarr7nfzbhifkgyf3dni4i3k4

On the Church-Rosser and coherence properties of conditional order-sorted rewrite theories

Francisco Durán, José Meseguer
2012 The Journal of Logic and Algebraic Programming  
conditional) rewrite rules.  ...  Given a rewrite theory R as above, we define the relation → R/A , either by the inference system of rewriting logic (see [9] ), or by the usual inductive description: → R/A = n → R/A,n , where → R/A,0  ...  We also thank Santiago Escobar for very fruitful discussion on the use of the narrowing library in Maude as a component of the CRC and ChC tools. F.  ... 
doi:10.1016/j.jlap.2011.12.004 fatcat:wua3gahbafbb3gz3u2g5ozj6j4

Twenty Years of Rewriting Logic [chapter]

José Meseguer
2010 Lecture Notes in Computer Science  
, probabilistic systems, bioinformatics and chemical systems.  ...  Rewriting logic is a simple computational logic that can naturally express both concurrent computation and logical deduction with great generality.  ...  As already mentioned, I feel a debt of gratitude to the many gifted researchers who have made important contributions to the rewriting logic research program.  ... 
doi:10.1007/978-3-642-16310-4_2 fatcat:ho7s76r67nc63bndpoptbh5k4e

Twenty years of rewriting logic

José Meseguer
2012 The Journal of Logic and Algebraic Programming  
, probabilistic systems, bioinformatics and chemical systems.  ...  Rewriting logic is a simple computational logic that can naturally express both concurrent computation and logical deduction with great generality.  ...  As already mentioned, I feel a debt of gratitude to the many gifted researchers who have made important contributions to the rewriting logic research program.  ... 
doi:10.1016/j.jlap.2012.06.003 fatcat:5tx4a5uxlvapfpf5fajozkbboi

Editors: Delia Kesner and Brigitte Pientka; Article No. 29

Christian Sternagel, Thomas Sternagel, Christian Sternagel, Thomas Sternagel
licensed under Creative Commons License CC-BY 1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016)   unpublished
Combining these two results and extending the conditional conflu-ence checker ConCon accordingly, we are able to automatically prove and certify confluence of an important class of conditional term rewrite  ...  Today there are a number of tools in existence which allow us to conveniently check various properties of standard term rewrite systems (TRSs).  ...  We thank Bertram Felgenhauer for producing at least 1.5 of our examples. We also thank the anonymous reviewers for their constructive and helpful comments.  ... 
fatcat:gjczqtl63vcv7dwwrivyk5ptju

LIPIcs, Volume 15, RTA'12, Complete Volume [article]

Ashish Tiwari
2013
the presentation of the final version.  ...  Acknowledgements: We would like to thank Roland Meyer for interesting discussions about several aspects of this work.  ...  The confluence conditions are necessary and sufficient for confluence of R 1 ∪ E ± . R TA ' 1 2 Deciding Confluence of Ground Term Rewrite Systems in Cubic Time Proof.  ... 
doi:10.4230/lipics.rta.2012 fatcat:i53phqg7yvahdovzjpatxgb7hq

Computational Air Traffic Management

Marc Anthony Azzopardi, James F. Whidborne
2011 2011 IEEE/AIAA 30th Digital Avionics Systems Conference  
The system offers unique advantages in terms of resilience to disruption, efficiency and future scalability.  ...  A specific embodiment of a CATM system was designed, constructed, simulated and tested and shown to be a significant step towards demonstrating the feasibility of a fully autonomous multi-agent-based air  ...  Although outside the scope of this dissertation, an agent model would allow the system to be analysed, verified and hence certified in terms of performance, robustness, correctness or utility of any subsystem  ... 
doi:10.1109/dasc.2011.6095967 fatcat:5kfu6ba5h5g7pdffh7z3ftdjai

Optimal market making under partial information and numerical methods for impulse control games with applications [article]

Diego Zabaljauregui
2020 arXiv   pre-print
A policy-iteration-type solver is proposed to solve an underlying system of quasi-variational inequalities, and it is validated numerically with reassuring results.  ...  The optimal full information spreads are shown to be biased when the exact market regime is unknown, as the market maker needs to adjust for additional regime uncertainty in terms of PnL sensitivity and  ...  General system of quasi-variational inequalities To present the system of QVIs derived in [ABC + 19], we need to define first the intervention operators.  ... 
arXiv:2009.06521v1 fatcat:4rymxg7bajg5dasz2bk7vbrlty

Case Studies, Counterfactuals, and Causal Explanations

Gregory Mitchell
2003 Social Science Research Network  
Application of a set of normative criteria to the products of these Enron thought experiments reveals the suspect nature of causal explanations and policy prescriptions drawn from  ...  The pitfalls of such thought experiments are illustrated through the discussion of the recent attempts to explain the collapse of Enron Corporation using this approach.  ...  these changes, decreases greatly.  ... 
doi:10.2139/ssrn.436682 fatcat:wlpj4jiwmrcm7c4vvfb34qukt4

Formal Methods and their Role in the Certification of Critical Systems [chapter]

John Rushby
1997 Safety and Reliability of Software Based Systems  
methods are offered in support of certification.  ...  This report was prepared to supplement a forthcoming chapter on formal methods in the FAA Digital Systems Validation Handbook 1 .  ...  In formal methods these particularly include my colleagues Friedrich von Henke, Sam Owre, and Shankar; and in safety-critical systems and their assessment, Ricky Butler of NASA Langley Research Center,  ... 
doi:10.1007/978-1-4471-0921-1_1 fatcat:33n3af7ssbfkbiy6o6vj462idi

Extending Implicit Computational Complexity and Abstract Machines to Languages with Control

Giulio <1984> Pellitta, Simone Martini
2014
Another is the possiblity to describe the execution of these programs in terms of abstract machines.  ...  One of the nice conseguences of this isomorphism is that we can reason about functional programs with formal tools which are typical of proof systems: such analysis can also include quantitative qualities  ...  Quasi-interpretations We consider first-order functional programs written as systems of terms with rewriting rules l → r.  ... 
doi:10.6092/unibo/amsdottorato/6558 fatcat:6t7pp4t77vartpg64we7yku56u

LIPIcs, Volume 188, TYPES 2020, Complete Volume [article]

Ugo de'Liguoro, Stefano Berardi, Thorsten Altenkirch
2021
the grammar of proof terms, the other being obtained by enriching the grammar of proof terms with a formal fixed-point operator to represent cyclic behaviour, the first calculus acting as the universe  ...  The approach is based on three main ideas: (i) the Curry-Howard paradigm of representation of proofs (by typed λ-terms) is extended to solutions of proof-search problems (a solution is a run of the proof  ...  Non-confluence excludes some techniques to show strong normalization, e.g., those that rely on deterministic weak head reduction.  ... 
doi:10.4230/lipics.types.2020 fatcat:qlbs2felejcvrfgqts3g7iyaqy

Права громадян на мирні зібрання: проблеми термінологічної невизначеності
Citizens'rights to peaceful meeting: problems of terminological uncertainty

O. Komissarov
2018 Naukovyy Visnyk Dnipropetrovs kogo Derzhavnogo Universytety Vnutrishnikh Sprav  
terms " the mass being of people", " the mass confluence of people" etc.  ...  The scientist determines the method of committing a crime as a system of actions for the preparation, commission and concealment of crimes, deterministic conditions of the environment and psychophysical  ...  in the system is Summary The author has analyzed current issues of implementation of the properties of the system of punishments in the process of law enforcement.  ... 
doi:10.31733/2078-3566-2018-2-101-104 fatcat:afi4hzgcu5drdod3ezhojgmzfi

An incremental prototyping methodology for distributed systems based on formal specifications

Jarle Hulaas
2005
This choice is guided by the completeness of the algorithm: It is correct given the assumption that the rewrite system satisfies termination and confluence, and it is capable of compiling conditional axioms  ...  Instead we will consider the specifications as conditional term rewriting systems, which means that the equations are oriented.  ...  As explained in chapter 4, rewriting is an interpretation of conditional equations which limits the semantics of algebraic specifications by orienting the equations.  ... 
doi:10.5075/epfl-thesis-1664 fatcat:bcs66bivo5cavlyehjxuq7t23q
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