This paper describes a general purpose program analysis that computes global control-ow and data-ow information for higher-order, call-by-value programs. This information can be used to drive global program optimizations such as inlining and run-time check elimination, as well as optimizations like constant folding and loop invariant code motion that are typically based on special-purpose local...

This paper describes a general purpose program analysis that computes global control-ow and data-ow information for higher-order, call-by-value programs. This information can be used to drive global program optimizations such as inlining and run-time check elimination, as well as optimizations like constant folding and loop invariant code motion that are typically based on special-purpose local...

Let w be a morphic word over a finite alphabet Σ, and let ∆ be a subalphabet. We study the behavior of maximal blocks of ∆ letters in w, and prove the following: let (ik, jk) denote the starting and ending positions, respectively, of the k’th maximal ∆-block in w. Then lim supk→∞(jk/ik) is algebraic if w is morphic, and rational if w is automatic. As a results, we show that the same holds if (i...

We prove, using a theorem of W. Schmidt, that if the sequence of partial quotients of the continued fraction expansion of a positive irrational real number takes only two values, and begins with arbitrary long blocks which are ''almost squares,'' then this number is either quadratic or transcendental. This result applies in particular to real numbers whose partial quotients form a Sturmian (or ...

Automatic sequences have many properties that other (in particular, non-uniformly morphic sequences) do not necessarily share. In this paper we survey a number of different methods can be used to prove given sequence is automatic. When the take their values in finite field Fq, also permits proving associated formal power series are transcendental over Fq(X).

Two finite words u, v are 2-binomially equivalent if, for all words x of length at most 2, the number of occurrences of x as a (scattered) subword of u is equal to the number of occurrences of x in v. This notion is a refinement of the usual abelian equivalence. A 2-binomial square is a word uv where u and v are 2-binomially equivalent. In this paper, considering pure morphic words, we prove th...

The authors establish the fundamental lemma for a relative trace formula. This trace formula compares generic automorphic representations of GSp(4) with auto-morphic representations of GL(4) which are distinguished with respect to a character of the Shalika subgroup, the subgroup of matrices of 2 × 2 block form g 0 X g. The fundamental lemma, giving the equality of two orbital integrals, amount...