CALL Statement
... The different, however, in the following respects: Functions are designed to return a single value to the program unit that references them. Subroutines often return more than one value, or they may return no value at all but simple perform some task such as displaying a list of instructions to the ...
... The different, however, in the following respects: Functions are designed to return a single value to the program unit that references them. Subroutines often return more than one value, or they may return no value at all but simple perform some task such as displaying a list of instructions to the ...
Introduction to Algorithms November 4, 2005
... consecutive non-promoted nodes that follow it in the list. For example, if the next node in the linked list is promoted, the count is 0; if the next node is not promoted, but the following node is promoted, the count is 1. The goal is to ensure that the count of a promoted node is at least and nomor ...
... consecutive non-promoted nodes that follow it in the list. For example, if the next node in the linked list is promoted, the count is 0; if the next node is not promoted, but the following node is promoted, the count is 1. The goal is to ensure that the count of a promoted node is at least and nomor ...
Slides - Computer Science, Columbia University
... Ways to store data so that computation can be done efficiently Most basic: variables, 1-d arrays Depending on the computational task, more sophisticated data structures can be helpful, with a tradeoff We’ll look at two very common data structures ...
... Ways to store data so that computation can be done efficiently Most basic: variables, 1-d arrays Depending on the computational task, more sophisticated data structures can be helpful, with a tradeoff We’ll look at two very common data structures ...
`Or` S - University of Windsor
... Monadic-Memoization (cont.) Memoization reduces worst-case time complexity from exponential to O(n3) The problem is Lazy-functional languages don’t let variable updating or keeping a global storage for the whole program Need to pass around the ‘Memo’ table so that All recursive parsing call ...
... Monadic-Memoization (cont.) Memoization reduces worst-case time complexity from exponential to O(n3) The problem is Lazy-functional languages don’t let variable updating or keeping a global storage for the whole program Need to pass around the ‘Memo’ table so that All recursive parsing call ...
Some Applications of Logic to Feasibility in Higher Types
... Then we say that F (f, ~x) is defined from functionals G, H by polynomially bounded recursion of polynomial length with bounds (Q, P ). As in definition 1.6, it is worth mentioning that neither the space bound Q(|f |, |~x|) nor the time bound P (|f |, |~x|) are basic feasible functionals. Theorem (3 ...
... Then we say that F (f, ~x) is defined from functionals G, H by polynomially bounded recursion of polynomial length with bounds (Q, P ). As in definition 1.6, it is worth mentioning that neither the space bound Q(|f |, |~x|) nor the time bound P (|f |, |~x|) are basic feasible functionals. Theorem (3 ...
PDF
... We briefly review the five standard systems of reverse mathematics. For completeness, we include systems stronger than arithmetical comprehension, but these will play no part in this paper. Details, general background, and results, as well as many examples of reversals, can be found in Simpson [1999 ...
... We briefly review the five standard systems of reverse mathematics. For completeness, we include systems stronger than arithmetical comprehension, but these will play no part in this paper. Details, general background, and results, as well as many examples of reversals, can be found in Simpson [1999 ...
Lecture 2. Marginal Functions, Average Functions - www
... lower output when marginal revenue is less than marginal cost. This makes sense, because, on the margin, profit goes up with x, if the extra revenue is greater than the extra cost and vice versa. The above marginal analysis can be extended to the case of finitely many choice variables. If the firm's ...
... lower output when marginal revenue is less than marginal cost. This makes sense, because, on the margin, profit goes up with x, if the extra revenue is greater than the extra cost and vice versa. The above marginal analysis can be extended to the case of finitely many choice variables. If the firm's ...
Prevent DNS Server from being used for a DoS attack
... 1. The attacker programs bots to continuously execute requests for this record against recursive DNS. 2. The bots spoof the source IP address of these requests, replacing it with the DDoS target. 3. The recursive servers take the record from the attacker-controlled zone, and send it along to the IP ...
... 1. The attacker programs bots to continuously execute requests for this record against recursive DNS. 2. The bots spoof the source IP address of these requests, replacing it with the DDoS target. 3. The recursive servers take the record from the attacker-controlled zone, and send it along to the IP ...
Mathematical Review - USC Upstate: Faculty
... By the definition of S(n): S(k+1) = S(k) + 2(k+1) = 2 (k+1) – 1 + 2(k+1) = 2. 2(k+1) – 1 = 2(k+2) – 1 ...
... By the definition of S(n): S(k+1) = S(k) + 2(k+1) = 2 (k+1) – 1 + 2(k+1) = 2. 2(k+1) – 1 = 2(k+2) – 1 ...
UNIFORMLY APPROACHABLE MAPS 1. Preliminaries Throughout
... let f : X → R. If there exists an uncountable Y ⊆ R such that f −1 (y) is non-empty and connected for every y ∈ Y and that ρ(f −1 (x), f −1 (y)) = 0 for every x, y ∈ Y then f is not W U A. Proof: Replacing X with f −1 (Y ), if necessary, we can assume that X = f −1 (Y ). Now, let D be a countable de ...
... let f : X → R. If there exists an uncountable Y ⊆ R such that f −1 (y) is non-empty and connected for every y ∈ Y and that ρ(f −1 (x), f −1 (y)) = 0 for every x, y ∈ Y then f is not W U A. Proof: Replacing X with f −1 (Y ), if necessary, we can assume that X = f −1 (Y ). Now, let D be a countable de ...
Document
... • Worry about one step • You expect too much from your at a time. friends. Each sub-instance must be • An abstraction within a smaller instance which to develop, think to the same problem. about, and describe algorithms in such way • You expect too much from your that their correctness is transparen ...
... • Worry about one step • You expect too much from your at a time. friends. Each sub-instance must be • An abstraction within a smaller instance which to develop, think to the same problem. about, and describe algorithms in such way • You expect too much from your that their correctness is transparen ...
Pointers to Functions - CS
... struct IntList; // intListNew() // Allocates a new list IntList* intListNew(); ...
... struct IntList; // intListNew() // Allocates a new list IntList* intListNew(); ...
We say f is strongly blending if, for any pair of
... apart (for the same iterate of f), and blending pulls far away points together (again, for the same iterate of f). Blending has certain obvious disadvantages when compared with transitivity. First and foremost, any function which is blending cannot be a homeomorphism, which automatically excludes th ...
... apart (for the same iterate of f), and blending pulls far away points together (again, for the same iterate of f). Blending has certain obvious disadvantages when compared with transitivity. First and foremost, any function which is blending cannot be a homeomorphism, which automatically excludes th ...
Sect_03_04_Notes
... b. Intuitive explanation about why you need lowest terms: for a vertical asymptote (x = c), as x gets closer and closer to c, you’ll end up with a smaller and smaller fraction, which is flipped-over in order to get a larger and larger number, thus the asymptote. (This reasoning can be flipped around ...
... b. Intuitive explanation about why you need lowest terms: for a vertical asymptote (x = c), as x gets closer and closer to c, you’ll end up with a smaller and smaller fraction, which is flipped-over in order to get a larger and larger number, thus the asymptote. (This reasoning can be flipped around ...
1 Divide and Conquer with Reduce
... Thought Experiment I: At some level, this problem seems like it can be solved using the divide-andconquer approach. Let’s try a simple pattern: divide up the input sequence in half, recursively solve each half, and “piece together” the solutions. A moment’s thought shows that the two recursive calls ...
... Thought Experiment I: At some level, this problem seems like it can be solved using the divide-andconquer approach. Let’s try a simple pattern: divide up the input sequence in half, recursively solve each half, and “piece together” the solutions. A moment’s thought shows that the two recursive calls ...
A Problem Course in Mathematical Logic Volume II Computability
... abstract models of computation in the 1930’s, including recursive functions, λ-calculus, Turing machines, and grammars. Although these models are very different from each other in spirit and formal definition, it turned out that they were all essentially equivalent in what they could do. This sugges ...
... abstract models of computation in the 1930’s, including recursive functions, λ-calculus, Turing machines, and grammars. Although these models are very different from each other in spirit and formal definition, it turned out that they were all essentially equivalent in what they could do. This sugges ...
Systematic Development of Programming Languages
... Every aspect of machine visible in program: – One statement per machine instruction. – Register allocation, call stack, etc. must be managed explicitly. No cs7100(Prasad) ...
... Every aspect of machine visible in program: – One statement per machine instruction. – Register allocation, call stack, etc. must be managed explicitly. No cs7100(Prasad) ...
Chapter 4 Methods
... uses if statements to check the filing status and computes the tax based on the filing status. This example uses functions to simplify Listing 3.4. Each filing status has six brackets. The code for computing taxes is nearly the same for each filing status except that each filing status has differen ...
... uses if statements to check the filing status and computes the tax based on the filing status. This example uses functions to simplify Listing 3.4. Each filing status has six brackets. The code for computing taxes is nearly the same for each filing status except that each filing status has differen ...
Lecture 11: Algorithms - United International College
... • Assume the different operations used in an algorithm take the same time, which simplifier the analysis. • Determine whether it is practical to use a particular algorithm to solve a problem as the size of the input increase • Compare two algorithms to determine which is more efficient as the size o ...
... • Assume the different operations used in an algorithm take the same time, which simplifier the analysis. • Determine whether it is practical to use a particular algorithm to solve a problem as the size of the input increase • Compare two algorithms to determine which is more efficient as the size o ...
Lecture 11: Functional Programming Concepts
... same parameter(s), it always returns the same result. •In mathematics all functions are referentially transparent •In programming this is not always the case, with use of imperative features in languages. • The subroutine/function called could affect some global variable that will cause a second inv ...
... same parameter(s), it always returns the same result. •In mathematics all functions are referentially transparent •In programming this is not always the case, with use of imperative features in languages. • The subroutine/function called could affect some global variable that will cause a second inv ...
Functions as Models
... 1. There are two different ’outputs’ (or y-values) for the ’input’ (or x-value) of 1. Because we cannot know whether 1 should go with 5 or 7 at any given time, this relation is not a function. 2. Since y = x, any time a number is chosen to represent x, that, and only that, number becomes y. From thi ...
... 1. There are two different ’outputs’ (or y-values) for the ’input’ (or x-value) of 1. Because we cannot know whether 1 should go with 5 or 7 at any given time, this relation is not a function. 2. Since y = x, any time a number is chosen to represent x, that, and only that, number becomes y. From thi ...
Notes on Simply Typed Lambda Calculus
... Computational information in that they can be see as functional programming languages, or more realistically, a solid core on which to build a functional language. Logical information in two ways. First, typed λ-calculi can be used directly as logics—these are ‘intuitionistic type theories’ such as ...
... Computational information in that they can be see as functional programming languages, or more realistically, a solid core on which to build a functional language. Logical information in two ways. First, typed λ-calculi can be used directly as logics—these are ‘intuitionistic type theories’ such as ...
PROBLEMS (solutions at end) Problem #1 The blue curve is the
... Is this region x-simple? Is it y-simple? Set up the integration if it is x-simple. Set up the integration if it is y-simple. Ans: The region is both x-simple and y-simple. The y-simple is the easiest, and leads to Int_{x = 0 to 2} Int_{y = |1-x| to 4 – x} f(x,y) dy dx. For the x-simple, the bounds d ...
... Is this region x-simple? Is it y-simple? Set up the integration if it is x-simple. Set up the integration if it is y-simple. Ans: The region is both x-simple and y-simple. The y-simple is the easiest, and leads to Int_{x = 0 to 2} Int_{y = |1-x| to 4 – x} f(x,y) dy dx. For the x-simple, the bounds d ...
EXTRA CREDIT PROJECTS The following extra credit projects are
... It turns out that there are many useful equivalent statements of the axiom of choice. Some versions, such as Tychonoff’s theorem and Zorn’s lemma, are in common use in many areas of mathematics. As the theoretical build-up needed to make sense of these versions of the axiom of choice is outside the ...
... It turns out that there are many useful equivalent statements of the axiom of choice. Some versions, such as Tychonoff’s theorem and Zorn’s lemma, are in common use in many areas of mathematics. As the theoretical build-up needed to make sense of these versions of the axiom of choice is outside the ...
ppt slides
... Replace the lowest one in the buffer if the input tuple is more than that. Takes O(n.K) time. Still low for a large n. ...
... Replace the lowest one in the buffer if the input tuple is more than that. Takes O(n.K) time. Still low for a large n. ...
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”.