The equational logic of fixed points
DOI10.1016/S0304-3975(96)00248-4zbMath0920.03067OpenAlexW2026410426MaRDI QIDQ1391734
Publication date: 22 July 1998
Published in: Theoretical Computer Science (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/s0304-3975(96)00248-4
surveyequational logiciteration theoriescomplete axiomatizationequational theoriesfixed-point identitiesproperties of fixed-point solutionsuniversal algebraic approach to the study of fixed points
Applications of universal algebra in computer science (08A70) Semantics in the theory of computing (68Q55) Categorical logic, topoi (03G30) Equational logic, Mal'tsev conditions (08B05) Theories (e.g., algebraic theories), structure, and semantics (18C10) Continuous lattices and posets, applications (06B35) Abstract and axiomatic computability and recursion theory (03D75)
Related Items
Uses Software
Cites Work
- Fixed-point operations on ccc's. I
- Fixed-point calculus
- Equational properties of Kleene algebras of relations with conversion
- A characterization of the least-fixed-point operator by dinaturality
- Solving reflexive domain equations in a category of complete metric spaces
- Fixed points in Cartesian closed categories
- Functorial polymorphism
- Algebras of iteration theories
- Recursion and iteration in continuous theories: the M-construction
- Results on the propositional \(\mu\)-calculus
- Fundamental properties of infinite trees
- A complete inference system for a class of regular behaviours
- Order and metric in the stream semantics of elemental concurrency
- Scott induction and closure under \(\omega\)-sups
- On flowchart theories. I. The deterministic case
- Monoides et semi-anneaux complets. (Complete monoids and semirings)
- On flowchart theories. II: The nondeterministic case
- Independence of the equational axioms for iteration theories
- Least fixed point of a functor
- Metric interpretations of infinite trees and semantics of non deterministic recursive programs
- Partially additive categories and flow-diagram semantics
- Unique fixed points vs. least fixed points
- Recursion-closed algebraic theories
- Regular trees and the free iterative theory
- Towards a foundation for semantics in complete metric spaces
- Complete systems of \(\mathcal B\)-rational identities
- A general result on abstract flowchart schemes with applications to the study of accessibility, reduction and minimization
- Models of a \(K\)-rational identity system
- Iteration theories of synchronization trees
- Chain-complete posets and directed sets with applications
- Algebraic structures for transitive closure
- Scalar and vector iteration
- Matricial theories
- On the algebraic structure of rooted trees
- On some classes of interpretations
- Fixed-point constructions in order-enriched categories
- A complete axiomatisation for observational congruence of finite-state behaviours
- A completeness theorem for Kleene algebras and the algebra of regular events
- A complete system of identities for one-letter rational expressions with multiplicities in the tropical semiring
- Notes on equational theories of relations
- Synchronization trees
- Nonaxiomatisability of equivalences over finite state processes
- Completeness of Park induction
- Categorical fixed point semantics
- Axiomatizing schemes and their behaviors
- Fixed points in free process algebras. I
- Equational logic of circular data type specification
- Representations of distributive lattice-ordered semigroups with binary relations
- Matrix and matricial iteration theories. I
- Matrix and matricial iteration theories. II
- A fixpoint theorem for complete categories
- Automata and languages generalized to \(\omega\)-continuous semirings
- A lattice-theoretical fixpoint theorem and its applications
- Predicate Transformer Semantics
- A Theorem on Partially Ordered Sets, With Applications to Fixed Point Theorems
- On a Theorem of R. Jungen
- Une remarque sur les systèmes complets d'identités rationnelles
- Varieties of Iteration Theories
- Solutions of the Iteration Equation and Extensions of the Scalar Iteration Operation
- Algebraic specification of data types: A synthetic approach
- Vector Iteration in Pointed Iterative Theories
- The Category-Theoretic Solution of Recursive Domain Equations
- Matrix versions of aperiodic $K$-rational identities
- Process Algebra
- Regular Algebra Applied to Path-finding Problems
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Data Types as Lattices
- Structured Programming With and Without go to Statements
- Initial Algebra Semantics and Continuous Algebras
- A menagerie of non-finitely based process semantics over BPA* – from ready simulation to completed traces
- Equational axioms for regular sets
- Step bisimulation is pomset equivalence on a parallel language without explicit internal choice
- Une condition impliquant toutes les identités rationnelles
- Processes and the denotational semantics of concurrency
- SOME EQUATIONAL LAWS OF INITIALITY IN 2CCC’S
- Categorical fixed point calculus
- Solving polynomial fixed point equations
- A completeness theorem for nondeterministic Kleene algebras
- Two Complete Axiom Systems for the Algebra of Regular Events
- On regular expressions and regular canonical systems
- Two Families of Languages Related to ALGOL
- FUNCTORIAL SEMANTICS OF ALGEBRAIC THEORIES
- Some quasi-varieties of iteration theories
- A complete axiomatisation for trace congruence of finite state behaviors
- On Kleene algebras