Results 1 
4 of
4
Algorithms: A quest for absolute definitions
 Bulletin of the European Association for Theoretical Computer Science
, 2003
"... y Abstract What is an algorithm? The interest in this foundational problem is not only theoretical; applications include specification, validation and verification of software and hardware systems. We describe the quest to understand and define the notion of algorithm. We start with the ChurchTurin ..."
Abstract

Cited by 20 (9 self)
 Add to MetaCart
y Abstract What is an algorithm? The interest in this foundational problem is not only theoretical; applications include specification, validation and verification of software and hardware systems. We describe the quest to understand and define the notion of algorithm. We start with the ChurchTuring thesis and contrast Church's and Turing's approaches, and we finish with some recent investigations.
Set Theory
"... Set Theory deals with the fundamental concepts of sets and functions used everywhere in mathematics. Cantor initiated the study of set theory with his investigations on the cardinality of sets of real numbers. In particular, he proved that there are different infinite cardinalities: the quantity of ..."
Abstract
 Add to MetaCart
Set Theory deals with the fundamental concepts of sets and functions used everywhere in mathematics. Cantor initiated the study of set theory with his investigations on the cardinality of sets of real numbers. In particular, he proved that there are different infinite cardinalities: the quantity of natural numbers is strictly smaller than the quantity of real numbers. Cantor formalized and studied the notions of ordinal and cardinal numbers. Set theory considers a universe of sets which is ordered by the membership or element relation ∈. All other mathematical objects are coded into this universe and studied within this framework. In this way, set theory is one of the foundations of mathematics. All of the information that will be covered by the exams can be found in this text, as well as most of the exercises that will be discussed in the tutorials. The grading scheme is as follows. • One final exam, worth 65%. • Two midterms, each worth 15%, for a total of 30%. • Three homework problems (explained below), each worth 1%, for a total of 3%. • Presentation of one problem in a tutorial, worth 2%. Each week, when exercises for the tutorials are handed out, some of them will be starred (∗). Each student must submit a solution to one starred problem assigned before the first midterm, one assigned between the first and second midterms and one assigned after the second midterm. These solutions must be carefully written up and submitted to J. Franklin by the tutorial for which they have been assigned. The other problems will not be graded. If you wish to know whether your solution is correct, you are welcome to submit these assignments to J. Franklin as well.
Set Theory
, 2010
"... Set Theory deals with the fundamental concepts of sets and functions used everywhere in mathematics. Cantor initiated the study of set theory with his investigations on the cardinality of sets of real numbers. In particular, he proved that there are different infinite cardinalities: the quantity of ..."
Abstract
 Add to MetaCart
Set Theory deals with the fundamental concepts of sets and functions used everywhere in mathematics. Cantor initiated the study of set theory with his investigations on the cardinality of sets of real numbers. In particular, he proved that there are different infinite cardinalities: the quantity of natural numbers is strictly smaller than the quantity of real numbers. Cantor formalized and studied the notions of ordinal and cardinal numbers. Set theory considers a universe of sets which is ordered by the membership or element relation ∈. All other mathematical objects are coded into this universe and studied within this framework. In this way, set theory is one of the foundations of mathematics. This text contains all information relevant for the exams. Furthermore, the exercises in this text are those which will be demonstrated in the tutorials. Each sheet of exercises contains some important ones marked with a star and some other ones. You have to hand in an exercise marked with a star in Weeks 3 to 6, Weeks 7 to 9 and Weeks 10 to 12; each of them gives one mark. Furthermore, you can hand in any further exercises, but they are only checked for correctness. There will be two mid term exams and a final exam; the mid term exams count 15 marks each and the final exam counts 67 marks.
Calculus Of Constituents A Decidable Fragment Of Second Order PL
"... Abstract — We present a short review of the calculus of constituents. We may think of symbolic logic as an attempt of syntactical description of some knowledge. Syntactical level is important because it is detached from interpretation, i.e. concrete meaning, thus, at least potentially, programable. ..."
Abstract
 Add to MetaCart
Abstract — We present a short review of the calculus of constituents. We may think of symbolic logic as an attempt of syntactical description of some knowledge. Syntactical level is important because it is detached from interpretation, i.e. concrete meaning, thus, at least potentially, programable. Here by