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A program logic for union bounds [article]

Gilles Barthe, Marco Gaboardi, Benjamin Grégoire, Justin Hsu, Pierre-Yves Strub
2016 arXiv   pre-print
We propose a probabilistic Hoare logic aHL based on the union bound, a tool from basic probability theory.  ...  While the union bound is simple, it is an extremely common tool for analyzing randomized algorithms.  ...  A union bound logic We will introduce a core imperative language with procedures and external procedures, which will form the setting for our program logic aHL.  ... 
arXiv:1602.05681v1 fatcat:zpih6evwfva6th7ysbqcn5pw5i

A Program Logic for Union Bounds *

Gilles Barthe, Marco Gaboardi, Benjamin Grégoire, Justin Hsu, Pierre-Yves Strub, S Gilles Barthe, Marco Gaboardi, Benjamin Grégoire, Justin Hsu, Pierre-Yves Strub
2016 licensed under Creative Commons License CC-BY 43rd International Colloquium on Automata, Languages, and Programming   unpublished
We propose a probabilistic Hoare logic aHL based on the union bound, a tool from basic probability theory.  ...  While the union bound is simple, it is an extremely common tool for analyzing randomized algorithms.  ...  A union bound logic Before introducing the program logic, we will begin by reviewing a largely standard, probabilistic imperative language.  ... 
fatcat:ysam6jvkdvapplsqtafklgrx3e

A lightweight symbolic virtual machine for solver-aided host languages

Emina Torlak, Rastislav Bodik
2013 Proceedings of the 35th ACM SIGPLAN Conference on Programming Language Design and Implementation - PLDI '14  
But reducing programming tasks to satisfiability problems involves translating programs to logical constraints, which is an engineering challenge even for domain-specific languages.  ...  This paper describes how to implement a symbolic virtual machine (SVM) for such a host language.  ...  Acknowledgments We thank Jeffrey Foster, Shaz Qadeer, and the anonymous reviewers for their comments on this paper.  ... 
doi:10.1145/2594291.2594340 dblp:conf/pldi/TorlakB14 fatcat:5r6setxj5rf4be3jrgm3vjdnba

A lightweight symbolic virtual machine for solver-aided host languages

Emina Torlak, Rastislav Bodik
2014 SIGPLAN notices  
But reducing programming tasks to satisfiability problems involves translating programs to logical constraints, which is an engineering challenge even for domain-specific languages.  ...  This paper describes how to implement a symbolic virtual machine (SVM) for such a host language.  ...  Acknowledgments We thank Jeffrey Foster, Shaz Qadeer, and the anonymous reviewers for their comments on this paper.  ... 
doi:10.1145/2666356.2594340 fatcat:du7xc3dttvhc3bhebst32w4ewi

Machine-Checked Verification of the Correctness and Amortized Complexity of an Efficient Union-Find Implementation [chapter]

Arthur Charguéraud, François Pottier
2015 Lecture Notes in Computer Science  
Moreover, we implement Union-Find as an OCaml library and formally endow it with a modular specification that offers a full functional correctness guarantee as well as an amortized complexity bound.  ...  Union-Find is a famous example of a simple data structure whose amortized asymptotic time complexity analysis is non-trivial. We present a Coq formalization of this analysis.  ...  There is a huge body of work on program verification using Separation Logic.  ... 
doi:10.1007/978-3-319-22102-1_9 fatcat:gnlvogowdbfhnlqfyiezy54m3q

Page 3367 of Mathematical Reviews Vol. , Issue 92f [page]

1992 Mathematical Reviews  
Motivations for studying this problem arise in logic programming memory management.”  ...  We present a new data structure which can support each operation in O(logn) time in the worst case. We prove that this bound is tight for pointer based algorithms.  ... 

Rules with Contextually Scoped Negation [chapter]

Axel Polleres, Cristina Feier, Andreas Harth
2006 Lecture Notes in Computer Science  
We also argue that this class of logic programs can be viewed as a rule extension to a subset of RDF(S).  ...  We propose logic programs with contexts and scoped negation and discuss two possible semantics with desirable properties.  ...  Acknowledgments The authors thank Jos de Bruijn, Rubén Lara, and Michael Kifer for fruitful discussions and the anonymous reviewers for their useful feedback.  ... 
doi:10.1007/11762256_26 fatcat:cu7jeceu5zd2vbu7ho24cxn5aa

Verifying the Correctness and Amortized Complexity of a Union-Find Implementation in Separation Logic with Time Credits

Arthur Charguéraud, François Pottier
2017 Journal of automated reasoning  
Separation Logic with Time Credits Separation Logic (Reynolds, 2002) offers a natural framework for proving the correctness of imperative programs that manipulate the heap.  ...  Coming back to Union-Find, we present a specification of Union-Find in Separation Logic with time credits ( §5).  ... 
doi:10.1007/s10817-017-9431-7 fatcat:opju5dkdmfcypel4zst5iuwcaq

Mind change complexity of learning logic programs

Sanjay Jain, Arun Sharma
2002 Theoretical Computer Science  
The present paper motivates the study of mind change complexity for learning minimal models of length-bounded logic programs.  ...  be a notation for the ÿrst limit ordinal.  ...  Acknowledgements We thank the anonymous referees for several helpful comments which improved the presentation of the paper.  ... 
doi:10.1016/s0304-3975(01)00084-6 fatcat:wconqudfuvaqbevfoxtfbiki6e

Logic Programs as Compact Denotations [chapter]

Patricia M. Hill, Fausto Spoto
2002 Lecture Notes in Computer Science  
We show that the time and space costs using logic programs for these analyses are smaller than those using a ground relational representation.  ...  The logic variables express regularity in the abstract behaviour of commands. The technique has been applied to sign, class and escape analysis for object-oriented programs.  ...  Related Work and Conclusion Non-ground logic programs have been used for the static analysis of both functional and logic programs.  ... 
doi:10.1007/3-540-36388-2_23 fatcat:kvcs75lljjhehc4pqn7u6ez2ze

Mind Change Complexity of Learning Logic Programs [chapter]

Sanjay Jain, Arun Sharma
1999 Lecture Notes in Computer Science  
The present paper motivates the study of mind change complexity for learning minimal models of length-bounded logic programs.  ...  [ASY92] showed that EFS can be viewed as a logic programming language over strings. Recently, various subclasses of EFS have been investigated in the context of learnability (e.g., see  ...  We thank the anonymous referees for several helpful comments which improved the presentation of the paper. The research of Sanjay Jain was supported in part by NUS grant number RP3992710.  ... 
doi:10.1007/3-540-49097-3_16 fatcat:qc3kyoumirhnbcf5w4wjojiwvu

Clausal Logic and Logic Programming in Algebraic Domains

William C Rounds, Guo-Qiang Zhang
2001 Information and Computation  
We establish the completeness of a resolutionrule for inferencein such a clausal logic; we introduce a natural declarative semantics and a xed-point semantics for disjunctive logic programs, and prove  ...  We introduce a domain-theoretic foundation for disjunctive logic programming. This foundation is built on clausal logic, a representation of the Smyth powerdomain of any coherent algebraic dcpo.  ...  We apply these results to give a xed-point semantics for abstract disjunctive logic programs.  ... 
doi:10.1006/inco.2001.3073 fatcat:k6gdk63x5remze6bguktcpqtty

A Mathematical Framework for Superintelligent Machines [article]

Daniel J. Buehrer
2018 arXiv   pre-print
INDEX TERMS 4-valued Boolean Logic, Artificial Intelligence, causal sets, class algebra, consciousness, intelligent design, IS-A hierarchy, mathematical logic, meta-theory, pointless topological space,  ...  For instance, it could check the black box of a car crash to determine if it was probably caused by electric failure, a stuck electronic gate, dark ice, or some other condition that it must add to its  ...  Its logic inference algorithm creates an IS-A hierarchy for classes, binary relations, and programs. This hierarchy is based on expressing every relation as a union of maximal bicliques.  ... 
arXiv:1804.03301v1 fatcat:nofcd7pfkjhmdhtiihkebostbu

Modular reasoning about heap paths via effectively propositional formulas

Shachar Itzhaky, Anindya Banerjee, Neil Immerman, Ori Lahav, Aleksandar Nanevski, Mooly Sagiv
2014 Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages - POPL '14  
By (a) requiring each procedure modifies a fixed set of heap partitions and creates a bounded amount of heap sharing, and (b) restricting program contracts and loop invariants to use only deterministic  ...  The restrictions force program specifications and verification conditions to lie within a fragment of first-order logic with transitive closure that is reducible to effectively propositional logic, and  ...  This bound is effective for all the procedure calls in prog; hence en B|A can be used in the restricted logic AE AR .  ... 
doi:10.1145/2535838.2535854 dblp:conf/popl/ItzhakyBILNS14 fatcat:tgycr5och5c43d4xgdggml7tbq

Page 207 of Southern Economic Journal Vol. 18, Issue 2 [page]

1951 Southern Economic Journal  
The second logical step in this program is the establishment of wage agreements based on equal pay for equal work in all plants and corporations doing comparable work within a section of our industry,  ...  In this pattern, bargaining bursts the bounds of a single industry and leaps abroad to span a number of industries.  ... 
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