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Mixed powerdomains for probability and nondeterminism [article]

Klaus Keimel, Gordon D. Plotkin
2017 arXiv   pre-print
We consider mixed powerdomains combining ordinary nondeterminism and probabilistic nondeterminism.  ...  We characterise them as free algebras for suitable (in)equation-al theories; we establish functional representation theorems; and we show equivalencies between state transformers and appropriately healthy  ...  Acknowledgements We are very grateful to Jean Goubault-Larrecq for his many helpful comments and suggestions.  ... 
arXiv:1612.01005v6 fatcat:2tuhxgaepvgp5c2ihwbucwktse

Probabilistic Completion of Nondeterministic Models

Guy Beaulieu
2007 Electronical Notes in Theoretical Computer Science  
This work continues ongoing research in combining theories of nondeterminism and probabilistic choice.  ...  Classically, models for mixed choice were obtained by enhancing arbitrary models for probabilistic choice with appropriately distributive nondeterministic operations.  ...  Finally, we present for each type of powerdomain for nondeterminism the corresponding posetal completion functor in order to build posetal models for mixed choice.  ... 
doi:10.1016/j.entcs.2007.02.028 fatcat:eldiddhlybb2dm55mqiqh4lrfu

Relating total and partial correctness interpretations of non-deterministic programs

Carl A. Gunter
1990 Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '90  
It is shown that the mixed powerdomain has many pleasing domain-theoretic and algebraic properties.  ...  The paper includes a sample non-deterministic programming language and a semantics using the mixed powcrdomain.  ...  Army Research Office Grant DAAG29-84-K-0061 and ONR contract number NOOO14-88-K-0557.  ... 
doi:10.1145/96709.96741 dblp:conf/popl/Gunter90 fatcat:6e5wxbtaqnbtzdvzupmwqablgq

The mixed powerdomain

Carl A. Gunter
1992 Theoretical Computer Science  
., The mixed power domain, Theoretical Computer Science 103 (1992) 311-334 This paper introduces an operator Ju called the mixed powerdomain which generalizes the convex (Plotkin) powerdomain.  ...  For a domain D with a coherent Scott topology, elements of .UD can be represented as pairs (U, V) where U E D is a compact upper set, V c D is a closed set and the downward closure of U n V is equal to  ...  Acknowledgements This paper was based on input and encouragement from a number of people.  ... 
doi:10.1016/0304-3975(92)90017-a fatcat:sfr3365wszhkhggrf5dsdkoigm

Basic Operational Preorders for Algebraic Effects in General, and for Combined Probability and Nondeterminism in Particular

Aliaume Lopez, Alex Simpson, Michael Wagner
2018 Annual Conference for Computer Science Logic  
We do this in the case of both angelic and demonic nondeterminism.  ...  in terms of Markov decision processes, denotational using a powerdomain, and axiomatic) all determine the same canonical preorder.  ...  Acknowledgements We thank Gordon Plotkin, Matija Pretnar and Niels Voorneveld for helpful discussions.  ... 
doi:10.4230/lipics.csl.2018.29 dblp:conf/csl/LopezS18 fatcat:wins7aui3bgvbkkwwv3hpp4z3e

Layout Randomization and Nondeterminism

Martín Abadi, Jérémy Planul, Gordon Plotkin
2013 Electronical Notes in Theoretical Computer Science  
This approach abstracts from language details, and helps manage the delicate interaction between probabilities and nondeterminism.  ...  We develop a semantic approach based on denotational models and simulation relations.  ...  Such a semantics could have the form: Mem → H V (Mem ξ⊥ ) mapping memories to probability distributions on memories, where H V is a powerdomain for mixed nondeterministic and probabilistic choice as discussed  ... 
doi:10.1016/j.entcs.2013.09.006 fatcat:42cdgecohnd6hnqtryne5wqwha

A theory for nondeterminism, parallelism, communication, and concurrency

Manfred Broy
1986 Theoretical Computer Science  
So the language allows to treat the basic semantic notions of nondeterminism, parallelism, communication, and concurrency for multiprogramming in a completely formal, applicative framework.  ...  An applicative language is introduced for representing concurrent programs and communicating systems in the form of mutually recursive systems of nondeterministic equations for functions and streams.  ...  But it even includes nondeterminism (for modelling the decision process of schedulers) and also allows the partial evaluation of expressions with free identifiers (cf. mixed computation in [37] ) and  ... 
doi:10.1016/0304-3975(86)90040-x fatcat:deaevefkgrc2nkg4qbcahq2bca

Contents and abstracts of the electronic notes in theoretical computer science vol. 6

1998 Theoretical Computer Science  
Y = [0, co] with usual addition and multiplication, reveals a close connection to the powerdomain of extended probability measures.  ...  The usual cut rule does not make sense for sequents which connect different logical systems because it mixes formulas from antecedent and succedent.  ...  information systems, following the style of Scott; and (ii) to introduce, as a consequence of this representation, a generalized resolution method for an arbitrary Smyth powerdomain and show the soundness  ... 
doi:10.1016/s0304-3975(98)90019-6 fatcat:cmxyrjlnjjae7gtbakg6dufkya

Formalized, Effective Domain Theory in Coq [chapter]

Robert Dockins
2014 Lecture Notes in Computer Science  
., products, sums, the function space, and powerdomains) are all developed. In addition, I build the machinery necessary to compute solutions to recursive domain equations.  ...  In particular, I develop constructive models of both the unpointed profinite and the pointed profinite domains.  ...  Sophisticated combinations of strict and nonstrict features can be built using the adjunction functors U and L, and nondeterminism may be modeled using the powerdomains.  ... 
doi:10.1007/978-3-319-08970-6_14 fatcat:3lbibth4mvfrhh77g5wxdlt6qq

Layout Randomization and Nondeterminism [chapter]

Martín Abadi, Jérémy Planul, Gordon D. Plotkin
2014 Lecture Notes in Computer Science  
This approach abstracts from language details, and helps manage the delicate interaction between nondeterminism and probability.  ...  any notion of probabilistic powerdomain.  ...  Such a semantics could have the form: Mem → H V (Mem ξ⊥ ) mapping memories to probability distributions on memories, where H V is a powerdomain for mixed nondeterministic and probabilistic choice as discussed  ... 
doi:10.1007/978-3-319-06880-0_1 fatcat:xbmbwjl2kjdd7j2pjdzvqjhamq

Healthiness Conditions for Predicate Transformers

Klaus Keimel
2015 Electronical Notes in Theoretical Computer Science  
One looks for necessary and, if possible, sufficient conditions (healthiness conditions) on predicate transformers that correspond to state transformers t: X → T Y .  ...  the desired property for the output.  ...  Our methods can be applied to quite some examples in the literature, in particular for nondeterminism and probability [4, 5, 9, 13, 14, 15, 16, 18, 21, 25] .  ... 
doi:10.1016/j.entcs.2015.12.016 fatcat:shapvv54rzc77nrywpn3zt5hfa

The convex powerdomain in a category of posets realized by cpos [chapter]

Alex K. Simpson
1995 Lecture Notes in Computer Science  
We construct a powerdomain in a category whose objects are posets of data equipped with a cpo of \intensional" representations of the data, and whose morphisms are those monotonic functions between posets  ...  Indeed we show that the powerdomain has interesting computational properties that di er from those of the usual convex powerdomain on cpos.  ...  Acknowledgements I would like to thank Pietro Di Gianantonio, Andy Pitts and Gordon Plotkin for their encouragement and for a number of helpful suggestions.  ... 
doi:10.1007/3-540-60164-3_23 fatcat:cl4ptere5zez3lhulkqhmli35i

Security, Probability and Nearly Fair Coins in the Cryptographers' Café [chapter]

Annabelle McIver, Larissa Meinicke, Carroll Morgan
2009 Lecture Notes in Computer Science  
Security and probability are both artefacts that we hope to bring increasingly within the reach of refinement-based Formal Methods; although we have worked on them separately, in the past, the goal has  ...  and abstraction all at once.  ...  nondeterminism and security.  ... 
doi:10.1007/978-3-642-05089-3_5 fatcat:v37xoiqsqrbxfgeynhqd6m2h4a

Choquet–Kendall–Matheron theorems for non-Hausdorff spaces

2011 Mathematical Structures in Computer Science  
This typical result of random set theory is profitably recast in purely topological terms, using intuitions and tools from domain theory.  ...  We obtain three variants of the theorem, each one characterizing distributions, in the form of continuous valuations, over relevant powerdomains of demonic, resp. angelic, resp. erratic non-determinism  ...  It was suggested that it should be given more visibility, and deserved a paper of its own. We thank Achim Jung for giving us the opportunity to do so.  ... 
doi:10.1017/s0960129510000617 fatcat:ppzbijmjvbfdbp5exndhsy7pey

A Convenient Category of Domains

Ingo Battenfeld, Matthias Schröder, Alex Simpson
2007 Electronical Notes in Theoretical Computer Science  
It also supports the construction of free algebras for (in)equational theories, can be used as the basis for a theory of computability, and provides a model of parametric polymorphism.  ...  We motivate and define a category of topological domains, whose objects are certain topological spaces, generalising the usual ω-continuous dcppos of domain theory.  ...  We also thank the anonymous referee for helpful suggestions.  ... 
doi:10.1016/j.entcs.2007.02.004 fatcat:tfvmwjta3bghfip63xew2onqvi
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