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Rectilinearization of functions definable by a Weierstrass system and its applications

Krzysztof Jan Nowak
2010 Annales Polonici Mathematici  
This paper presents several theorems on the rectilinearization of functions definable by a convergent Weierstrass system, as well as their applications to decomposition into special cubes and quantifier  ...  N N201 372336 from the Polish Ministry of Science and Higher Education.  ...  Several theorems concerning rectilinearization of quasi-subanalytic functions are provided in Section 2.  ... 
doi:10.4064/ap99-2-2 fatcat:iaenbancnverxklcv2ma3n3gei

Synchronization of Finite Automata: Contributions to an Old Problem [chapter]

Arto Salomaa
2002 Lecture Notes in Computer Science  
The present paper investigates this and related problems within the general framework of a composition theory for functions over a finite domain N with n elements.  ...  Our results show that the study of functions of several variables may shed light also to the case where all functions considered are unary.  ...  With the following sections in mind, the next definition is stated for functions with several variables. The variables still range over the set N , and also the function values are in N .  ... 
doi:10.1007/3-540-36377-7_3 fatcat:5ve3wxhe45fohhexf2j77kytda

Page 451 of Mathematical Reviews Vol. 26, Issue 3 [page]

1963 Mathematical Reviews  
Salomaa, Arto 2356 A theorem concerning the composition of functions of several variables ranging over a finite set. J. Symbolic Logic 25 (1960), 203-208 (1962).  ...  A function g is said to be generated by a set F of functions if g can be expressed as a finite composition of functions in F.  ... 

Verification of the Completeness of Unification Algorithms à la Robinson [chapter]

Andréia B. Avelar, Flávio L. C. de Moura, André Luiz Galdino, Mauricio Ayala-Rincón
2010 Lecture Notes in Computer Science  
The methodology is based on a previously developed formalization of the theorem of existence of most general unifiers for unifiable terms over first-order signatures.  ...  This work presents a general methodology for verification of the completeness of firstorder unification algorithmsà la Robinson developed in the higher-order proof assistant PVS.  ...  range terms whose variables also range in this set and that conform a set of variables disjoint from the domain.  ... 
doi:10.1007/978-3-642-13824-9_10 fatcat:ne54gywxnre4jpqld5mosc5fkm

Composition sequences for functions over a finite domain

Arto Salomaa
2003 Theoretical Computer Science  
Diverse problems ranging from many-valued logics to ÿnite automata can be expressed as questions concerning compositions of functions over a ÿnite domain.  ...  Many of the very basic problems turn out to be NP-hard. Also several open problems are pointed out.  ...  D C (f) = max(D(F; f)); but now F ranges over complete sets of functions.  ... 
doi:10.1016/s0304-3975(01)00227-4 fatcat:ysa7sqmxhjepnkphjjh4j6uy3q

The Arity Gap of Polynomial Functions over Bounded Distributive Lattices

Miguel Couceiro, Erkko Lehtonen
2010 2010 40th IEEE International Symposium on Multiple-Valued Logic  
Let A and B be arbitrary sets with at least two elements. The arity gap of a function f: A^n \to B is the minimum decrease in its essential arity when essential arguments of f are identified.  ...  In this paper we study the arity gap of polynomial functions over bounded distributive lattices and present a complete classification of such functions in terms of their arity gap.  ...  It is easily observed that gap f = min i =j (ess f − ess f i←j ), where i and j range over the set of indices of essential variables of f .  ... 
doi:10.1109/ismvl.2010.29 dblp:conf/ismvl/CouceiroL10 fatcat:5ccf3jori5anxhjgadswadrksq

Page 3680 of Mathematical Reviews Vol. , Issue 89G [page]

1989 Mathematical Reviews  
The theorem of Tsen-Lang says that if F is an algebraically closed field then K is a C,,-field, i.e., any homogeneous polynomial of degree d over K with more than d" variables has a nontriv- ial solution  ...  Emphasis is on the use of the CRAY-1 and CRAY-2 supercomput- ers as a mighty tool to provide insight based on results obtained “several orders of magnitude” beyond the range of smaller ma- chines.  ... 

Learning Read-Constant Polynomials of Constant Degree Modulo Composites

Arkadev Chattopadhyay, Ricard Gavaldà, Kristoffer Arnsfelt Hansen, Denis Thérien
2013 Theory of Computing Systems  
Boolean functions that have constant degree polynomial representation over a fixed finite ring form a natural and strict subclass of the complexity class ACC 0 .  ...  the additional constraint that each variable in the target polynomial appears in a constant number of monomials.  ...  Chattopadhyay was at the University of Toronto when this work was written up, partially supported by a Natural Sciences and Engineering Research Council (NSERC) postdoctoral fellowship, an Ontario Ministry  ... 
doi:10.1007/s00224-013-9488-6 fatcat:fal6fnzso5dcfligtvyswc5f4i

Learning Read-Constant Polynomials of Constant Degree Modulo Composites [chapter]

Arkadev Chattopadhyay, Ricard Gavaldà, Kristoffer Arnsfelt Hansen, Denis Thérien
2011 Lecture Notes in Computer Science  
Boolean functions that have constant degree polynomial representation over a fixed finite ring form a natural and strict subclass of the complexity class ACC 0 .  ...  the additional constraint that each variable in the target polynomial appears in a constant number of monomials.  ...  Chattopadhyay was at the University of Toronto when this work was written up, partially supported by a Natural Sciences and Engineering Research Council (NSERC) postdoctoral fellowship, an Ontario Ministry  ... 
doi:10.1007/978-3-642-20712-9_3 fatcat:zzpp2pg73bbz5hupfozuy6vdgu

Page 1029 of Mathematical Reviews Vol. 54, Issue 4 [page]

1977 Mathematical Reviews  
i¢ xja,=B,, j<m of m linear equations in 7 variables, where the a, and the b, are positive ordinals and the variables x, range over ordinals.  ...  It follows from the previous work of Benda, Ketonen and Kanamori that under the assumption of the theorem, these functions must dominate (on a stationary set) every function from w, into w,.  ... 

Page 3002 of Mathematical Reviews Vol. , Issue 84h [page]

1984 Mathematical Reviews  
The author shows that the least intermediate logic containing both L( K) and L(M), where K and M range over finite sets of finite trees, is of the form L(N) for some finite set N of finite trees.  ...  finite sets of finite trees forms a sublattice of the lattice of all intermediate logics.  ... 

Alfred Tarski and undecidable theories

George F. McNulty
1986 Journal of Symbolic Logic (JSL)  
Over the ensuing fifty-five years, Tarski put forth a steady stream of theorems concerning decidability, many with far-reaching consequences.  ...  Just as the work of the 1926 seminar reflected Tarski's profound early interest in decidability, so does his last work, A formalization of set theory without variables , a monograph written in collaboration  ...  in place of x < y and by restricting the variables to range over the set defined by * (x).  ... 
doi:10.2307/2273902 fatcat:iav44bpgjrgztkhoxpotrfruge

The April meeting of the American Mathematical Society at Chicago

Arnold Dresden
1917 Bulletin of the American Mathematical Society  
Let {F[0, 1, 2, • • -, n; i^i*™- •]} (fc = 1, 2, • • •) be a set of iterative compositions of a function of n + 1 variables (n = 1, 2, 3, • • •), the variables in the entire set being notationally distinct  ...  to a class §, of the three variables p', p" and x, which range over the classes ty' and ^3" (general classes) and 36 (a linear interval) re- 2.  ...  MCEWEN: "Determination of the functional relation between one variable and each of a number of correlated variables by successive approximation." (4) Professor W. A.  ... 
doi:10.1090/s0002-9904-1917-02974-6 fatcat:trnl2jh7hvf5roh6ymz3qkss6y

Arithmetical Composition and Inversion of Functions Over Classes

E. T. Bell
1931 Transactions of the American Mathematical Society  
It is noteworthy that a comprehensive theory, among whose instances are several extensive theories of numerical functions, many of which have themselves a high degree of generality, should be comprised  ...  If one or more of the postulates of a field be modified ( §13), contradicted ( §12), or suppressed ( §5), and if the altered set of postulates be selfconsistent, the set defines what we shall call a variety  ...  Composition as required for the purpose outlined in §7 is concerned with functions of matric variables.  ... 
doi:10.2307/1989515 fatcat:7e2v5t3hrfhvbmlvui6asprf3m

Arithmetical composition and inversion of functions over classes

E. T. Bell
1931 Transactions of the American Mathematical Society  
It is noteworthy that a comprehensive theory, among whose instances are several extensive theories of numerical functions, many of which have themselves a high degree of generality, should be comprised  ...  If one or more of the postulates of a field be modified ( §13), contradicted ( §12), or suppressed ( §5), and if the altered set of postulates be selfconsistent, the set defines what we shall call a variety  ...  Composition as required for the purpose outlined in §7 is concerned with functions of matric variables.  ... 
doi:10.1090/s0002-9947-1931-1501623-x fatcat:xxdltxrl4bdafbpdwm2j4hosmu
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