Andr E Arnold
ثبت نشده
چکیده
In 1986, Niwi nski 13] showed that the alternation hierarchy of the-calculus on binary trees without intersection was strict. But the xed-point terms he considered for proving this result are all equivalent to coB uchi terms (i.e. in 2) with intersection. Since then, the question of the strictness of the hierarchy of the-calculus on binary trees with intersection was open 4, 14]. Recently, and simultaneously, Braddeld 5] and Lenzi 9] have proved that the alternation hierarchy of the modal-calculus is strict. In 6], Braddeld shows that the formula n ^ i=1 (R i) x i)) ^ (O) ] n ^ i=1 (R i) x i)); that states that the rst player has a winning strategy in a parity game 16] and that is nothing but the extension of the Emerson-Jutla's formula 7] to games that are not bipartite. The Lenzi's n-and n-hard formulas are formulas on n-ary trees. They are deened inductively by L 0 (P) = L d 0 (P) = P; L n+1 (P) = x n+1 :(P ^ L d n (a n+1 :x n+1)); L d n+1 (P) = x n+1 :(P _ L n (a n+1 :x n+1)); where a node has property a i :x if its ith successor has property x. Since Lenzi's formulas are formulas on n-ary trees, and since one can encode n-ary trees into binary trees, one can deduce from Lenzi's result that the alternation hierarchy of the-calculus is also strict on binary trees. Such a transformation is not so easy for Braddeld's and Walukiewicz's formulas. In this note we ooer a direct proof that Walukiewicz's formulas are hard on binary trees. It combines two arguments used by Braddeld in 6]:
منابع مشابه
e–Quillen cohomology of commutative S-algebras
We de ne topological Andr e–Quillen cohomology of commutative S-algebras and construct a spectral sequence that calculates the Andr e–Quillen cohomology of commutative S-algebras over HFp. c © 1999 Elsevier Science B.V. All rights reserved.
متن کاملFrom Route Descriptions to Sketches: A Model for a Text-to-Image Translator
This paper deals with the automatic translation of route descriptions into graphic sketches. We discuss some general problems implied by such inter-mode transcription. We propose a model for an automatic text-to-image translator with a two-stage intermediate representation in which the linguistic representation of a route description precedes the creation of its conceptual representation. 1 I n...
متن کاملHomotopy and Homology of Simplicial Abelian Hopf Algebras
Let A be a simplicial bicommutative Hopf algebra over the eld F 2 with the property that 0 A = F 2. We show that A is a functor of the Andr e-Quillen homology of A, where A is regarded as an F 2 algebra. Then we give a method for calculating that Andr e-Quillen homology independent of knowledge of A.
متن کاملAndrographolide Protects against Aortic Banding-Induced Experimental Cardiac Hypertrophy by Inhibiting MAPKs Signaling
Despite therapeutic advances, heart failure-related mortality rates remain high. Therefore, understanding the pathophysiological mechanisms involved in the remodeling process is crucial for the development of new therapeutic strategies. Andrographolide (Andr), a botanical compound, has potent cardio-protective effects due to its ability to inhibit mitogen-activated protein kinases (MAPKs). Andr...
متن کاملThe Klinefelter syndrome: current management and research challenges.
E. Nieschlag, A. Ferlin, C. H. Gravholt, J. Gromoll, B. K€ ohler, H. Lejeune, A. D. Rogol and J. Wistuba Centre of Reproductive Medicine and Andrology, University of M€ unster, M€ unster, Germany, Centre of Excellence in Genomic Medicine Research, King Abdulaziz University, Jeddah, Saudi Arabia, Unit of Andrology and Reproductive Medicine, Department of Medicine, University of Padova, Padova, I...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1999