PPT - UBC Department of CPSC Undergraduates
... Every logical equivalence that we’ve learned applies to predicate logic statements. For example, to prove ~x D, P(x), you can prove x D, ~P(x) and then convert it back with generalized De Morgan’s. To prove x D, P(x) Q(x), you can prove x D, ~Q(x) ~P(x) and convert it back using the ...
... Every logical equivalence that we’ve learned applies to predicate logic statements. For example, to prove ~x D, P(x), you can prove x D, ~P(x) and then convert it back with generalized De Morgan’s. To prove x D, P(x) Q(x), you can prove x D, ~Q(x) ~P(x) and convert it back using the ...
Document
... Able to tell what an algorithm is and have some understanding why we study algorithms ...
... Able to tell what an algorithm is and have some understanding why we study algorithms ...
STUDY ON ELLIPTIC AND HYPERELLIPTIC CURVE METHODS
... • 2nd Step largely increases the probability that factors are found with a small increase in running time. Second, we investigated factoring using hyperelliptic curves through experiments. Using hyperelliptic curves for factoring is analyzed by Lenstra, Pila and Pomerance [8] from theoretical intere ...
... • 2nd Step largely increases the probability that factors are found with a small increase in running time. Second, we investigated factoring using hyperelliptic curves through experiments. Using hyperelliptic curves for factoring is analyzed by Lenstra, Pila and Pomerance [8] from theoretical intere ...
Recent Progress on the Complexity of Solving Markov Decision
... algorithm, we have Tφk+1 vφk = T vφk ≥ vφk , which by induction implies that Tφnk+1 vφk ≥ T vφk for every n ∈ N. Letting n → ∞, this means vφk+1 ≥ T vφk on each iteration k; by induction, this implies that the k th policy produced by the algorithm satisfies vφk ≥ T k vφ0 , where φ0 is the initial po ...
... algorithm, we have Tφk+1 vφk = T vφk ≥ vφk , which by induction implies that Tφnk+1 vφk ≥ T vφk for every n ∈ N. Letting n → ∞, this means vφk+1 ≥ T vφk on each iteration k; by induction, this implies that the k th policy produced by the algorithm satisfies vφk ≥ T k vφ0 , where φ0 is the initial po ...
GigaTensor: Scaling Tensor Analysis Up By 100 Times
... tensors (having attracted best paper awards, e.g. see [20]). However, the toolboxes have critical restrictions: 1) they operate strictly on data that can fit in the main memory, and 2) their scalability is limited by the scalability of Matlab. In [4, 20], efficient ways of computing tensor decomposi ...
... tensors (having attracted best paper awards, e.g. see [20]). However, the toolboxes have critical restrictions: 1) they operate strictly on data that can fit in the main memory, and 2) their scalability is limited by the scalability of Matlab. In [4, 20], efficient ways of computing tensor decomposi ...
On the Classification and Algorithmic Analysis of Carmichael Numbers
... The results pertaining to the classification of Carmichael numbers with a proportion of Fermat witnesses of less than 50% are detailed in Section 3.1. This classification provides a lower bound for the smallest prime factor of certain Carmichael numbers with a proportion of Fermat witnesses of less ...
... The results pertaining to the classification of Carmichael numbers with a proportion of Fermat witnesses of less than 50% are detailed in Section 3.1. This classification provides a lower bound for the smallest prime factor of certain Carmichael numbers with a proportion of Fermat witnesses of less ...
4 slides/page
... ◦ To find a 100-digit prime; ∗ Keep choosing odd numbers at random ∗ Check if they are prime (using fast randomized primality test) ∗ Keep trying until you find one ∗ Roughly 100 attempts should do it ...
... ◦ To find a 100-digit prime; ∗ Keep choosing odd numbers at random ∗ Check if they are prime (using fast randomized primality test) ∗ Keep trying until you find one ∗ Roughly 100 attempts should do it ...
Addition and Subtraction
... In order to be able to do addition more quickly, mathematicians create an algorithm – a process to follow that will produce a guaranteed result. Many of you already know some algorithms, but we will introduce a few different algorithms. When you encounter a problem, having more than one set of tools ...
... In order to be able to do addition more quickly, mathematicians create an algorithm – a process to follow that will produce a guaranteed result. Many of you already know some algorithms, but we will introduce a few different algorithms. When you encounter a problem, having more than one set of tools ...
Algorithm
In mathematics and computer science, an algorithm (/ˈælɡərɪðəm/ AL-gə-ri-dhəm) is a self-contained step-by-step set of operations to be performed. Algorithms exist that perform calculation, data processing, and automated reasoning.An algorithm is an effective method that can be expressed within a finite amount of space and time and in a well-defined formal language for calculating a function. Starting from an initial state and initial input (perhaps empty), the instructions describe a computation that, when executed, proceeds through a finite number of well-defined successive states, eventually producing ""output"" and terminating at a final ending state. The transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate random input.The concept of algorithm has existed for centuries, however a partial formalization of what would become the modern algorithm began with attempts to solve the Entscheidungsproblem (the ""decision problem"") posed by David Hilbert in 1928. Subsequent formalizations were framed as attempts to define ""effective calculability"" or ""effective method""; those formalizations included the Gödel–Herbrand–Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church's lambda calculus of 1936, Emil Post's ""Formulation 1"" of 1936, and Alan Turing's Turing machines of 1936–7 and 1939. Giving a formal definition of algorithms, corresponding to the intuitive notion, remains a challenging problem.