A programming language for the inductive sets, and applications
Information and Control
Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
Concurrent Processes and Their Syntax
Journal of the ACM (JACM)
Ten Years of Hoare's Logic: A Survey—Part I
ACM Transactions on Programming Languages and Systems (TOPLAS)
A Weaker Precondition for Loops
ACM Transactions on Programming Languages and Systems (TOPLAS)
Mathematical Theory of Program Correctness
Mathematical Theory of Program Correctness
First-Order Dynamic Logic
Semantics of Unbounded Nondeterminism
Proceedings of the 7th Colloquium on Automata, Languages and Programming
Characterizing Correctness Properties of Parallel Programs Using Fixpoints
Proceedings of the 7th Colloquium on Automata, Languages and Programming
A Cook's Tour of Countable Nondeterminism
Proceedings of the 8th Colloquium on Automata, Languages and Programming
On the Semantics of Fair Parallelism
Proceedings of the Abstract Software Specifications, 1979 Copenhagen Winter School
Dijkstras Predicate Transformers & Smyth's Power Domaine
Proceedings of the Abstract Software Specifications, 1979 Copenhagen Winter School
Semantics of Nondeterministic and Noncontinuous Constructs
Program Construction, International Summer Schoo
Denotational semantics of concurrency
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Specification and verification of concurrent programs by A∀automata
POPL '87 Proceedings of the 14th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Fairness in parallel programs: the transformational approach
ACM Transactions on Programming Languages and Systems (TOPLAS)
A generalization of Dijkstra's calculus
ACM Transactions on Programming Languages and Systems (TOPLAS)
Progress measures and stack assertions for fair termination
PODC '92 Proceedings of the eleventh annual ACM symposium on Principles of distributed computing
Inductive definitions, semantics and abstract interpretations
POPL '92 Proceedings of the 19th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Adding fair choice to Dijkstra's calculus
ACM Transactions on Programming Languages and Systems (TOPLAS)
Algebraic approaches to nondeterminism—an overview
ACM Computing Surveys (CSUR)
Making abstract interpretations complete
Journal of the ACM (JACM)
A characterization of symmetric semantics by domain complementation
Proceedings of the 2nd ACM SIGPLAN international conference on Principles and practice of declarative programming
Readings in hardware/software co-design
Constructive design of a hierarchy of semantics of a transition system by abstract interpretation
Theoretical Computer Science
Soundness of data refinement for a higher-order imperative language
Theoretical Computer Science
Uncountable limits and the lambda calculus
Nordic Journal of Computing
Temporal concurrent constraint programming: denotation, logic and applications
Nordic Journal of Computing
Unique Fixed Point Induction for McCarthy's Amb
MFCS '99 Proceedings of the 24th International Symposium on Mathematical Foundations of Computer Science
On the Semantics of Refinement Calculi
FOSSACS '00 Proceedings of the Third International Conference on Foundations of Software Science and Computation Structures: Held as Part of the Joint European Conferences on Theory and Practice of Software,ETAPS 2000
Polynomial Constants Are Decidable
SAS '02 Proceedings of the 9th International Symposium on Static Analysis
Hoare Logics for Recursive Procedures and Unbounded Nondeterminism
CSL '02 Proceedings of the 16th International Workshop and 11th Annual Conference of the EACSL on Computer Science Logic
POPL '84 Proceedings of the 11th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
A general result on infinite trees and its applications
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Non-Standard Semantics for Program Slicing
Higher-Order and Symbolic Computation
Precise interprocedural analysis through linear algebra
Proceedings of the 31st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Precise interprocedural dependence analysis of parallel programs
Theoretical Computer Science
Computing polynomial program invariants
Information Processing Letters
Transforming semantics by abstract interpretation
Theoretical Computer Science
Dually nondeterministic functions
ACM Transactions on Programming Languages and Systems (TOPLAS)
Hiding Software Watermarks in Loop Structures
SAS '08 Proceedings of the 15th international symposium on Static Analysis
A domain equation for bisimulation
Information and Computation
Alternating states for dual nondeterminism in imperative programming
Theoretical Computer Science
Reasoning about loops in total and general correctness
UTP'08 Proceedings of the 2nd international conference on Unifying theories of programming
Semantics and proof rules of invariant based programs
Proceedings of the 2011 ACM Symposium on Applied Computing
Bidomains and full abstraction for countable nondeterminism
FOSSACS'06 Proceedings of the 9th European joint conference on Foundations of Software Science and Computation Structures
Non-termination in unifying theories of programming
RelMiCS'05 Proceedings of the 8th international conference on Relational Methods in Computer Science, Proceedings of the 3rd international conference on Applications of Kleene Algebra
Separation logic for higher-order store
CSL'06 Proceedings of the 20th international conference on Computer Science Logic
Interprocedural herbrand equalities
ESOP'05 Proceedings of the 14th European conference on Programming Languages and Systems
| Hi-index | 0.01 |
Four semantics for a small programming language involving unbounded (but countable) nondeterminism are provided. These comprise an operational semantics, two state transformation semantics based on the Egli-Milner and Smyth orders, respectively, and a weakest precondition semantics. Their equivalence is proved. A Hoare-like proof system for total correctness is also introduced and its soundness and completeness in an appropriate sense are shown. Finally, the recursion theoretic complexity of the notions introduced is studied. Admission of countable nondeterminism results in a lack of continuity of various semantic functions, and this is shown to be necessary for any semantics satisfying appropriate conditions. In proofs of total correctness, one resorts to the use of (countable) ordinals, and it is shown that all recursive ordinals are needed.