Lecture 8: Back-and-forth - to go back my main page.
... Putting together various facts from previous lectures gives us a converse to Proposition 8.1. Proposition 8.13. Let M |= I∆0 + exp in which a complete type is coded if and only if it is realized. Then M is recursively saturated. 6 N because according to our definition, all sets in SSy(N) Proof sketc ...
... Putting together various facts from previous lectures gives us a converse to Proposition 8.1. Proposition 8.13. Let M |= I∆0 + exp in which a complete type is coded if and only if it is realized. Then M is recursively saturated. 6 N because according to our definition, all sets in SSy(N) Proof sketc ...
Overview of Leda Programming Language
... The overall program structure of a Leda program is a series of zero or more declarations followed by a single compound statement making up the body of the program. Comments are supported within the program text by use of the curly brackets. The include special statement in Leda allows the attachment ...
... The overall program structure of a Leda program is a series of zero or more declarations followed by a single compound statement making up the body of the program. Comments are supported within the program text by use of the curly brackets. The include special statement in Leda allows the attachment ...
Chapter 4 Measurable Functions
... It is necessary to prove that the three parts of the definition of measurability of a function are consistent. Exercise 4.1.1. Show that if f : X → R is A-measurable, then f −1 (G) ∈ A for every open set G ⊆ R. Show that the concepts of measurability in Definition 4.1.1 for both real and complex va ...
... It is necessary to prove that the three parts of the definition of measurability of a function are consistent. Exercise 4.1.1. Show that if f : X → R is A-measurable, then f −1 (G) ∈ A for every open set G ⊆ R. Show that the concepts of measurability in Definition 4.1.1 for both real and complex va ...
Self Modifying Cartesian Genetic Programming: Finding algorithms
... As in CGP, in SMCGP each node in the directed graph represents a particular function and is encoded by a number of genes. The first gene encodes the function of the node. This is followed by a number of connection genes (as in CGP) that indicate the location in the graph where the node takes its inp ...
... As in CGP, in SMCGP each node in the directed graph represents a particular function and is encoded by a number of genes. The first gene encodes the function of the node. This is followed by a number of connection genes (as in CGP) that indicate the location in the graph where the node takes its inp ...
Introduction to Cloud Computing Functional Programming and MapReduce Iliano Cervesato
... A Functional Programming Example in C Functional programming is not an attribute of the language but a state of mind ...
... A Functional Programming Example in C Functional programming is not an attribute of the language but a state of mind ...
Convergent Temporal-Difference Learning with Arbitrary Smooth
... attempt to solve this problem by performing gradient descent on the Bellman error. However, unlike TD, these algorithms usually require two independent samples from each state. Moreover, even if two samples are provided, the solution to which they converge may not be desirable (Sutton et al., 2009b ...
... attempt to solve this problem by performing gradient descent on the Bellman error. However, unlike TD, these algorithms usually require two independent samples from each state. Moreover, even if two samples are provided, the solution to which they converge may not be desirable (Sutton et al., 2009b ...
Levels of Abstraction
... symbols instead of binary digits to describe fields of instructions. Every aspect of machine visible in program: – One statement per machine instruction. – Register allocation, call stack, etc. must be managed explicitly. No ...
... symbols instead of binary digits to describe fields of instructions. Every aspect of machine visible in program: – One statement per machine instruction. – Register allocation, call stack, etc. must be managed explicitly. No ...
1 Solutions to assignment 3, due May 31
... 9. Problem 9.24 Consider the two function f1 (x) = x2 and f2 (x) = x. Then these are both increasing (and continuous!) functions (and thus are injective) which satisfy fi (0) = 0 and fi (1) = 1. Thus they are (by the intermediate value theorem) surjective, i.e. bijective. 10. Problem 9.25 This follo ...
... 9. Problem 9.24 Consider the two function f1 (x) = x2 and f2 (x) = x. Then these are both increasing (and continuous!) functions (and thus are injective) which satisfy fi (0) = 0 and fi (1) = 1. Thus they are (by the intermediate value theorem) surjective, i.e. bijective. 10. Problem 9.25 This follo ...
Memoizing Top-Down Backtracking Left
... Like any other parsers, they can be used for both parsing Natural languages (English) or Formal languages (Java). Though combinatory parsers were introduced by Burge in 1975, it was Wadler (1985) who first popularized the use of combinatory parsers. Combinatory parsers are written and used within th ...
... Like any other parsers, they can be used for both parsing Natural languages (English) or Formal languages (Java). Though combinatory parsers were introduced by Burge in 1975, it was Wadler (1985) who first popularized the use of combinatory parsers. Combinatory parsers are written and used within th ...
A Review of C Programming
... System namespace partitioning (avoid name clashes) Implementing shared services or data ...
... System namespace partitioning (avoid name clashes) Implementing shared services or data ...
Split-Ordered Lists: Lock-Free Extensible Hash Tables
... Current architectures support basic compare-and-swap (CAS) atomicity, which does not support atomic movement of even a single item. To circumvent this, the authors propose a solution based on the following idea; rather than moving the items among the buckets, they move the buckets among the items. I ...
... Current architectures support basic compare-and-swap (CAS) atomicity, which does not support atomic movement of even a single item. To circumvent this, the authors propose a solution based on the following idea; rather than moving the items among the buckets, they move the buckets among the items. I ...
PDF
... We can imagine a simpler principle if we work in a sub-logic in which we do not keep track of all the evidence. This kind of sub-logic is called classical logic, and we will examine it more later in the course. {Least Number Principle:} ∃x : N.A(x) ⇒ ∃y : N.(A(y)&∀z : N.z < y ⇒∼ A(z)). There are man ...
... We can imagine a simpler principle if we work in a sub-logic in which we do not keep track of all the evidence. This kind of sub-logic is called classical logic, and we will examine it more later in the course. {Least Number Principle:} ∃x : N.A(x) ⇒ ∃y : N.(A(y)&∀z : N.z < y ⇒∼ A(z)). There are man ...
Readable, writable, both, or neither? A programming language that
... Donald Knuth wrote “The art of programming,” "father" of the analysis of algorithms, big O notation ...
... Donald Knuth wrote “The art of programming,” "father" of the analysis of algorithms, big O notation ...
Primitive Recursive Arithmetic and its Role in the Foundations of
... preferable to accept the notion of function as sui generis, to interpret A → B simply as the domain of functions from A to B, and to understand equations between objects of such a type to mean equality in the usual sense of extensional equality of functions. What makes T constructive is not that it ...
... preferable to accept the notion of function as sui generis, to interpret A → B simply as the domain of functions from A to B, and to understand equations between objects of such a type to mean equality in the usual sense of extensional equality of functions. What makes T constructive is not that it ...
Functional Programming
... • Problematic point, because Haskell intends to preserve referential transparency. – An expression is said to be referentially transparent if it can be replaced with its value without changing the program. – Referential transparency requires the same results for a given set of arguments at any point ...
... • Problematic point, because Haskell intends to preserve referential transparency. – An expression is said to be referentially transparent if it can be replaced with its value without changing the program. – Referential transparency requires the same results for a given set of arguments at any point ...
Slide
... • Problematic point, because Haskell intends to preserve referential transparency. – An expression is said to be referentially transparent if it can be replaced with its value without changing the program. – Referential transparency requires the same results for a given set of arguments at any point ...
... • Problematic point, because Haskell intends to preserve referential transparency. – An expression is said to be referentially transparent if it can be replaced with its value without changing the program. – Referential transparency requires the same results for a given set of arguments at any point ...
Lab 9 lecture slides
... A window with the title Python 3.4.4rc1 Shell should appear. This window is the Shell. If the window does not appear, click on Start and then in the box Search programs and files write IDLE. A list will appear. Click on IDLE(Python 3.4 GUI-64 bit). A window with the title Python 3.4.4rc1 should appe ...
... A window with the title Python 3.4.4rc1 Shell should appear. This window is the Shell. If the window does not appear, click on Start and then in the box Search programs and files write IDLE. A list will appear. Click on IDLE(Python 3.4 GUI-64 bit). A window with the title Python 3.4.4rc1 should appe ...
Lecture notes from 5860
... of the statements that can be derived by means of the formal rules (or, what amounts to the same, how they are understood) because understanding a language, even a formal one, is not merely to understand its rules as rules of symbol manipulation. Believing that is the mistake of formalism.” The firs ...
... of the statements that can be derived by means of the formal rules (or, what amounts to the same, how they are understood) because understanding a language, even a formal one, is not merely to understand its rules as rules of symbol manipulation. Believing that is the mistake of formalism.” The firs ...
Extended Analog Computer and Turing machines - Hektor
... And now we can write our main result. Theorem 10. For any Turing machine there exist some EAC which can robustly simulate it. Proof. This proof is based on the construction from [10]. Let : ℕ3 ℕ be the transition function of the Turing machine M, under the encoding described above. To iterate the ...
... And now we can write our main result. Theorem 10. For any Turing machine there exist some EAC which can robustly simulate it. Proof. This proof is based on the construction from [10]. Let : ℕ3 ℕ be the transition function of the Turing machine M, under the encoding described above. To iterate the ...
ppt - Dave Reed
... O(N log N) sorts there are sorting algorithms that do better than insertion & selection sorts merge sort & quick sort are commonly used O(N log N) sorts recall from sequential vs. binary search examples: when N is large, log N is much smaller than N thus, when N is large, N log N is much smalle ...
... O(N log N) sorts there are sorting algorithms that do better than insertion & selection sorts merge sort & quick sort are commonly used O(N log N) sorts recall from sequential vs. binary search examples: when N is large, log N is much smaller than N thus, when N is large, N log N is much smalle ...
Name_______________ MAC 2233 Marginal Analysis Worksheet 1.
... 3. (Tan, section 3.4 problem 5) Custom Office makes a line of executive desks. It is estimated that the total cost for making x units of their Senior Executive model is dollars per year. a. Find the average cost function, ...
... 3. (Tan, section 3.4 problem 5) Custom Office makes a line of executive desks. It is estimated that the total cost for making x units of their Senior Executive model is dollars per year. a. Find the average cost function, ...
ppt
... Implement the Quicksort algorithm by completing the split() function as well as other code for input and output. - (Step 1) Implement & test the input & output code, e.g., to read numbers into an array and print numbers from an array. - (Step 2) Implement & test the split() function (without the sor ...
... Implement the Quicksort algorithm by completing the split() function as well as other code for input and output. - (Step 1) Implement & test the input & output code, e.g., to read numbers into an array and print numbers from an array. - (Step 2) Implement & test the split() function (without the sor ...
A Tutorial Introduction to the Lambda Calculus
... The more confusing part of standard λ calculus, when first approaching it, is the fact that we do not give names to functions. Any time we want to apply a function, we write the whole function definition and then procede to evaluate it. To simplify the notation, however, we will use capital letters, ...
... The more confusing part of standard λ calculus, when first approaching it, is the fact that we do not give names to functions. Any time we want to apply a function, we write the whole function definition and then procede to evaluate it. To simplify the notation, however, we will use capital letters, ...
Dynamic Programming
... We have seen some algorithm design principles, such as divide-and-conquer, brute force, and greedy Brute force is widely applicable, but inefficient Divide-and-conquer and greedy are fast, but only applicable on very specific problems. Dynamic Programming is somewhere in between them, while still pr ...
... We have seen some algorithm design principles, such as divide-and-conquer, brute force, and greedy Brute force is widely applicable, but inefficient Divide-and-conquer and greedy are fast, but only applicable on very specific problems. Dynamic Programming is somewhere in between them, while still pr ...
Section 4 - Introduction Handout
... the derivatives from the left and right of point a are both ∞ and –∞ or they are equal to -∞ and ∞. The slopes are both infinities but not the same infinity. Average Rate of Change (Slope of a Secant Line) The average rates of change of f ( x ) with respect to x for a function f as x changes from a ...
... the derivatives from the left and right of point a are both ∞ and –∞ or they are equal to -∞ and ∞. The slopes are both infinities but not the same infinity. Average Rate of Change (Slope of a Secant Line) The average rates of change of f ( x ) with respect to x for a function f as x changes from a ...
Recursion (computer science)
Recursion in computer science is a method where the solution to a problem depends on solutions to smaller instances of the same problem (as opposed to iteration). The approach can be applied to many types of problems, and recursion is one of the central ideas of computer science.""The power of recursion evidently lies in the possibility of defining an infinite set of objects by a finite statement. In the same manner, an infinite number of computations can be described by a finite recursive program, even if this program contains no explicit repetitions.""Most computer programming languages support recursion by allowing a function to call itself within the program text. Some functional programming languages do not define any looping constructs but rely solely on recursion to repeatedly call code. Computability theory proves that these recursive-only languages are Turing complete; they are as computationally powerful as Turing complete imperative languages, meaning they can solve the same kinds of problems as imperative languages even without iterative control structures such as “while” and “for”.