Coinductive counting with weighted automata

A general methodology is developed to compute the solution of a wide variety of basic counting problems in a uniform way: (1) the objects to be counted are enumerated by means of an infinite weighted automaton; (2) the automaton is reduced by means of the quantitative notion of stream bisimulation; (3) the reduced automaton is used to compute

Enumeration of kk-Fibonacci Paths using Infinite Weighted Automata

In this paper, we introduce a new family of generalized colored Motzkin paths, where horizontal steps are colored by means of $F_{k,l}$ colors, where $F_{k,l}$ is the $l$th $k$-Fibonacci number. We study the enumeration of this family according to the length. For this, we use infinite weighted automata.Comment: arXiv admin note: substantial text overlap with arXiv:1310.244

Coalgebraic semantics of heavy-weighted automata

We study heavy-weighted automata, a generalization of weighted automata in which the weights of the transitions can be any formal power series. We define their semantics in three equivalent ways, and give some examples of how they can provide a more compact representation of certain power series than ordinary weighted automata

Coalgebraic semantics of heavy-weighted automata

We study heavy-weighted automata, a generalization of weighted automata in which the weights of the transitions can be any formal power series. We define their semantics in three equivalent ways, and give some examples of how they can provide a more compact representation of certain power series than ordinary weighted automata

Coalgebraic semantics of heavy-weighted automata

We study heavy-weighted automata, a generalization of weighted automata in which the weights of the transitions can be any formal power series. We define their semantics in three equivalent ways, and give some examples of how they can provide a more compact representation of certain power series than ordinary weighted automata

Coalgebraic semantics of heavy-weighted automata

We study heavy-weighted automata, a generalization of weighted automata in which the weights of the transitions can be any formal power series. We define their semantics in three equivalent ways, and give some examples of how they can provide a more compact representation of certain power series than ordinary weighted automata

Coinductive counting : bisimulation in enumerative combinatorics

The recently developed coinductive calculus of streams finds here a further application in enumerative combinatorics. A general methodology is developed to solve a wide variety of basic counting problems in a uniform way: (1) the objects to be counted are enumerated by means of an infinite (weighted) automaton; (2) the automaton is minimized b

QStream: A Suite of Streams

We present a simple tool in Haskell, QStream, implementing the technique of coinductive counting by making use of Haskell's built-in coinduction capabilities. We furthermore provide a number of useful tools for stream exploration, including a number of pretty print functions and integration with the Online Encyclopedia of Integer Sequences