Algebraic approaches to program semantics
Algebraic approaches to program semantics
Automatic Sequences: Theory, Applications, Generalizations
Automatic Sequences: Theory, Applications, Generalizations
Journal of Automata, Languages and Combinatorics - Special issue: Selected papers of the workshop weighted automata: Theory and applications (Dresden University of Technology (Germany), March 4-8, 2002)
Behavioural differential equations: a coinductive calculus of streams, automata, and power series
Theoretical Computer Science
A coinductive calculus of streams
Mathematical Structures in Computer Science
Observational Coalgebras and Complete Sets of Co-operations
Electronic Notes in Theoretical Computer Science (ENTCS)
Circular Coinduction with Special Contexts
ICFEM '09 Proceedings of the 11th International Conference on Formal Engineering Methods: Formal Methods and Software Engineering
Bisimulations Generated from Corecursive Equations
Electronic Notes in Theoretical Computer Science (ENTCS)
Information and Computation
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We study the set TA of infinite binary trees with nodes labelled in a semiring A from a coalgebraic perspective. We present coinductive definition and proof principles based on the fact that TA carries a final coalgebra structure. By viewing trees as formal power series, we develop a calculus where definitions are presented as behavioural differential equations. We present a general format for these equations that guarantees the existence and uniqueness of solutions. Although technically not very difficult, the resulting framework has surprisingly nice applications, which is illustrated by various concrete examples.