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On the cost and complexity of the successor function
- In Proc. WORDS 2007
, 2009
"... Abstract. For a given numeration system, the successor function maps the representation of an integer n onto the representation of its successor n+1. In a general setting, the successor function maps the n-th word of a genealogically ordered language L onto the (n+1)-th word of L. We show that, if t ..."
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Cited by 4 (3 self)
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Abstract. For a given numeration system, the successor function maps the representation of an integer n onto the representation of its successor n+1. In a general setting, the successor function maps the n-th word of a genealogically ordered language L onto the (n+1)-th word of L. We show that, if the ratio of the number of elements of length n +1overthenumber of elements of length n of the language has a limit β>1, then the amortized cost of the successor function is equal to β/(β − 1). From this, we deduce the value of the amortized cost for several classes of numeration systems (integer base systems, canonical numeration systems associated with a Parry number, abstract numeration systems built on a rational language, and rational base numeration systems). 1
Rational base number systems for p-adic numbers
"... Abstract. This paper deals with rational base number systems for p-adic numbers. We mainly focus on the system proposed by Akiyama, Frougny, and Sakarovitch in 2008, but we also show that this system is in some sense isomorphic to other ones. We identify the numbers with finite and eventually period ..."
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Abstract. This paper deals with rational base number systems for p-adic numbers. We mainly focus on the system proposed by Akiyama, Frougny, and Sakarovitch in 2008, but we also show that this system is in some sense isomorphic to other ones. We identify the numbers with finite and eventually periodic representations and we also determine the number of representations of a given p-adic number. 1
Available online at: www.rairo-ita.org RATIONAL BASE NUMBER SYSTEMS FOR p-ADIC NUMBERS
"... Abstract. This paper deals with rational base number systems for p-adic numbers. We mainly focus on the system proposed by Akiyama et al. in 2008, but we also show that this system is in some sense isomorphic to some other rational base number systems by means of finite transducers. We identify the ..."
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Abstract. This paper deals with rational base number systems for p-adic numbers. We mainly focus on the system proposed by Akiyama et al. in 2008, but we also show that this system is in some sense isomorphic to some other rational base number systems by means of finite transducers. We identify the numbers with finite and eventually periodic representations and we also determine the number of representations of a given p-adic number. Mathematics Subject Classification. 11A67, 11E95. 1.
