Abstract and concrete categories
Abstract and concrete categories
Minimization of rational word functions
SIAM Journal on Computing
A proof of Choffrut's theorem on subsequential functions
Theoretical Computer Science
Universal coalgebra: a theory of systems
Theoretical Computer Science - Modern algebra and its applications
Re-describing an algorithm by Hopcroft
Theoretical Computer Science
Automata, Languages, and Machines
Automata, Languages, and Machines
Automata and Computability
Introduction to Automata Theory, Languages and Computability
Introduction to Automata Theory, Languages and Computability
Automata and Algebras in Categories
Automata and Algebras in Categories
Determinization of transducers over finite and infinite words
Theoretical Computer Science
Minimizing subsequential transducers: a survey
Theoretical Computer Science
A Generalization of Ginsburg and Rose's Characterization of G-S-M Mappings
Proceedings of the 6th Colloquium, on Automata, Languages and Programming
Subsequential Functions: Characterizations, Minimization, Examples
Proceedings of the 6th International Meeting of Young Computer Scientists on Aspects and Prospects of Theoretical Computer Science
Automata and Coinduction (An Exercise in Coalgebra)
CONCUR '98 Proceedings of the 9th International Conference on Concurrency Theory
A note on coinduction and weak bisimilarity for while programs
A note on coinduction and weak bisimilarity for while programs
Behavioural differential equations: a coinductive calculus of streams, automata, and power series
Theoretical Computer Science
Coalgebraic modal logic: soundness, completeness and decidability of local consequence
Theoretical Computer Science
Finite-state transducers in language and speech processing
Computational Linguistics
A hierarchy of probabilistic system types
Theoretical Computer Science - Selected papers of CMCS'03
Speech and Language Processing (2nd Edition)
Speech and Language Processing (2nd Edition)
Coalgebraising Subsequential Transducers
Electronic Notes in Theoretical Computer Science (ENTCS)
An Algebra for Kripke Polynomial Coalgebras
LICS '09 Proceedings of the 2009 24th Annual IEEE Symposium on Logic In Computer Science
Weak Bisimulation for Action-Type Coalgebras
Electronic Notes in Theoretical Computer Science (ENTCS)
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Subsequential transducers combine (input) language recognition with transduction and thereby generalise classic deterministic automata as well as Mealy and Moore type state machines. These well known subclasses all have a natural coalgebraic characterisation, and the question arises whether their coalgebraic modelling can be extended to subsequential transducers and their underlying structures. In this paper, we show that although subsequential structures cannot generally be regarded as coalgebras, the subclass of normalised structures do form a subcategory of coalgebras. Moreover, normalised structures are reflective in the category of all subsequential structures, and a final normalised structure exists. The existence and properties of the minimal subsequential transducer can be derived from this result. We also show that for the class of subsequential structures in which all states are accepting, an alternative coalgebraic representation is obtained by taking differentials. This differential representation gives rise to a new method of deciding equivalence and computing minimal representations which does not involve normalisation. Both normalisation and taking differentials can be formalised as functors into reflective subcategories of coalgebras, and we can therefore see these constructions as coalgebraisation.