We solve a conjecture of J. Shallit related to the automaticity function of a unary language, or equivalently to the first occurrence function in a symbolic sequence. The answer is negative: the conjecture is false, but it can be corrected by changing the constant involved. The proof is based on a study of paths in the Rauzy graphs associated to the sequence
AbstractWe focus on infinite words with languages closed under reversal. If frequencies of all facto...
Streams are omnipresent in both mathematics and theoretical computer science. Automatic sequences fo...
Under the motto “Paving the way towards Human-Centric AI”International audienceIn the field of patte...
AbstractBlanchard and Fabre (1994) have considered description of symbolic systems by sequences obta...
Automatic sequences are sequences which are produced by a finite automaton. Although they are not ra...
International audienceWe conjecture that bounded generalised polynomial functions cannot be generate...
AbstractWe revisit a technique of S. Lehr on automata and use it to prove old and new results in a s...
AbstractDirichlet series whose coefficients are generated by finite automata define meromorphic func...
Automatic structures are countable structures finitely presentable by a collection of automata. We s...
Almost a century ago, Presburger showed that the first order theory of the natural numbers with addi...
An automatic sequence is a letter-to-letter coding of a fixed point of a uniform morphism. More gene...
Almost a century ago, Presburger showed that the first order theory of the natural numbers with addi...
We discuss the use of negative bases in automatic sequences. Recently the theorem-prover Walnut has ...
summary:We show a connection between a recent conjecture of Shallit and an older conjecture of Rauzy...
An integer sequence {a n } is called polynomially recursive, or P-recursive, if it satisfies a nontr...
AbstractWe focus on infinite words with languages closed under reversal. If frequencies of all facto...
Streams are omnipresent in both mathematics and theoretical computer science. Automatic sequences fo...
Under the motto “Paving the way towards Human-Centric AI”International audienceIn the field of patte...
AbstractBlanchard and Fabre (1994) have considered description of symbolic systems by sequences obta...
Automatic sequences are sequences which are produced by a finite automaton. Although they are not ra...
International audienceWe conjecture that bounded generalised polynomial functions cannot be generate...
AbstractWe revisit a technique of S. Lehr on automata and use it to prove old and new results in a s...
AbstractDirichlet series whose coefficients are generated by finite automata define meromorphic func...
Automatic structures are countable structures finitely presentable by a collection of automata. We s...
Almost a century ago, Presburger showed that the first order theory of the natural numbers with addi...
An automatic sequence is a letter-to-letter coding of a fixed point of a uniform morphism. More gene...
Almost a century ago, Presburger showed that the first order theory of the natural numbers with addi...
We discuss the use of negative bases in automatic sequences. Recently the theorem-prover Walnut has ...
summary:We show a connection between a recent conjecture of Shallit and an older conjecture of Rauzy...
An integer sequence {a n } is called polynomially recursive, or P-recursive, if it satisfies a nontr...
AbstractWe focus on infinite words with languages closed under reversal. If frequencies of all facto...
Streams are omnipresent in both mathematics and theoretical computer science. Automatic sequences fo...
Under the motto “Paving the way towards Human-Centric AI”International audienceIn the field of patte...
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