It is well-known that Sturmian sequences are the non ultimately periodic sequences that are balanced over a 2-letter alphabet. They are also characterized by their complexity: they have exactly (n + 1) distinct factors of length n. A natural generalization of Sturmian sequences is the set of infinite episturmian sequences. These sequences are not necessarily balanced over a k-letter alphabet, n...

We compute the cardinality of the syntactic monoid of the language 0∗ repb(mN) made of base b expansions of the multiples of the integer m. We also give lower bounds for the syntactic complexity of any (ultimately) periodic set of integers written in base b. We apply our results to a well studied problem: decide whether or not a b-recognizable set of integers is ultimately periodic.

Lucy-n is a language for programming networks of processes communicating through bounded buffers. A dedicated type system, termed a clock calculus, automatically computes static schedules of the processes and the sizes of the buffers between them. In this article, we present a new algorithm which solves the subtyping constraints generated by the clock calculus. The advantage of this algorithm i...

Consider a non-standard numeration system like the one built over the Fibonacci sequence where nonnegative integers are represented by words over {0, 1} without two consecutive 1. Given a set X of integers such that the language of their greedy representations in this system is accepted by a finite automaton, we consider the problem of deciding whether or not X is a finite union of arithmetic p...

Incremental SAT solving under assumptions, introduced in Minisat, is in wide use. However, Minisat’s algorithm for incremental SAT solving under assumptions has two main drawbacks which hinder performance considerably. First, it is not compliant with the highly effective and commonly used preprocessor SatELite. Second, all the assumptions are left in the formula, rather than being represented a...

We present two new algorithms FastAccSum and FastPrecSum, one to compute a faithful rounding of the sum of floating-point numbers and the other for a result “as if” computed in K-fold precision. Faithful rounding means the computed result either is one of the immediate floating-point neighbors of the exact result or is equal to the exact sum if this is a floating-point number. The algorithms ar...