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Movie Title Year Distributor Notes Rev Formats Adult Video News Awards 1992 1992 VCA Buttman's Award Winning Orgies 1997 Evil Angel 3 DRO Buttman's Butt Freak 1 1992 Evil Angel Anal 2 DRO Buttman's European Vacation 1 1991 Evil Angel Facial 3 DRO Ebony Love 1992 Video Team O Femme Fatal 1993 Magma Girls Of Sin 1994 Pleasure Productions Lethal Passion 1991 Sunshine Films 1 D Lez Be Friends 1992 Video Team LezOnly DRO Making of Metamorphose 1993 Magma Overtime: Dyke Overflow 1994 Video Team LezOnly
Overtime: Dyke Overflow 2 1995 Video Team LezOnly Raunch 4 1991 Coast To Coast Facial DRO Sean Michaels' On the Road 5 1993 Video Team Sean Michaels' On the Road 6 1993 Video Team Silver Elegance 1992 Video Team 1 Silver Seduction 1992 Video Team 2 DO Silver Sensation 1992 Video Team Sleepless Nights 1997 Leisure Time Entertainment Sterling Silver 1991 Coast To Coast Facial Teri Weigel & Silver: Their Hottest Boy/girl Scenes 1992 Video Team

but when resources (such as time or space) are bounded, some of these may be more powerful than others. A deterministic Turing machine is the most basic Turing machine, which uses a fixed set of rules to determine its future actions. A probabilistic Turing machine is a deterministic Turing machine with an extra supply of random bits. The ability to make probabilistic decisions often helps algorithms solve problems more efficiently. Algorithms that use random bits are called randomized algorithms. A non-deterministic Turing machine is a deterministic Turing machine with an added feature of non-determinism, which allows a Turing machine to have multiple possible future actions from a given state. One way to view non-determinism is that the Turing machine branches into many possible computational paths at each step, and if it solves the problem in any of these branches, it is said to have solved the problem. Clearly, this model is not meant to be a physically realizable model, it is just a theoretically interesting abstract machine that gives rise to particularly interesting complexity classes. For examples, see non-deterministic algorithm. Other machine models Many machine models different from the standard multi-tape Turing machines have been proposed in the literature, for example random access machines. Perhaps surprisingly, each of these models can be converted to another without providing any extra computational power. The time and memory consumption of these alternate models may vary.[2] What all these models have in common is that the machines operate deterministically. However, some computational problems are easier to analyze in terms of more unusual resources. For example, a non-deterministic Turing machine is a computational model that is allowed to branch out to check many different possibilities at once. The non-deterministic Turing machine has very little to do with how we physically want to compute algorithms, but its branching exactly captures many of the mathematical models we want to analyze, so that non-deterministic time is a very important resource in analyzing computational problems. Complexity measures For a precise definition of what it means to solve a problem using a given amount of time and space, a computational model such as the deterministic Turing machine is used. The time required by a deterministic Turing machine M on input x is the total number of state transitions, or steps, the machine makes before it halts and outputs the answer ("yes" or "no"). A Turing machine M is said to operate within time f(n) if the time required by M on each input of length n is at most f(n). A decision problem A can be solved in time f(n) if there exists a Turing machine operating in time f(n) that solves the problem. Since complexity theory is interested in classifying problems based on their difficulty, one defines sets of problems based on some criteria. For instance, the set of problems solvable within time f(n) on a deterministic Turing machine is then denoted by DTIME(f(n)). Analogous definitions can be made for space requirements. Although time and space are the most well-known complexity resources, any complexity measure can be viewed as a computational resource. Complexity measures are very generally defined by the Blum complexity axioms. Other complexity measures used in complexity theory include communication complexity, circuit complexity, and decision tree complexity. The complexity of an algorithm is often expressed using big O notation. Best, worst and average case complexity Visualization of the quicksort algorithm that has average case performance {\displaystyle {\mathcal {O}}(n\log n)}{\displaystyle {\mathcal {O}}(n\log n)}. The best, worst and average case complexity refer to three different ways of measuring the time complexity (or any other complexity measure) of different inputs of the same size. Since some inputs of size n may be faster to solve than others, we define the following complexities: Best-case complexity: This is the complexity of solving the problem for the best input of size n. Average-case complexity: This is the complexity of solving the problem on an average. This complexity is only defined with respect to a probability distribution over the inputs. For instance, if all inputs of the same size are assumed to be equally likely to appear, the average case complexity can be defined with respect to the uniform distribution over all inputs of size n. Amortized analysis: Amortized analysis considers both the costly and less costly operations together over the whole series of operations of the algorithm. Worst-case complexity: This is the complexity of solving the problem for the worst input of size n. The order from cheap to costly is: Best, average (of discrete uniform distribution), amortized, worst. For example, consider the deterministic sorting algorithm quicksort. This solves the problem of sorting a list of integers that is given as the input. The worst-case is when the input is sorted or sorted in reverse order, and the algorithm takes time O(n2) for this case. If we assume that all possible permutations of the input list are equally likely, the average time taken for sorting is O(n log n). The best case occurs when each pivoting divides the list in half, also needing O(n log n) time. Upper and lower bounds on the complexity of problems To classify the computation time (or similar resources, such as space consumption), it is helpful to demonstrate upper and lower bounds on the maximum amount of time required by the most efficient algorithm to solve a given problem. The complexity of an algorithm is usually taken to be its worst-case complexity, unless specified otherwise. Analyzing a particular algorithm falls under the field of analysis of algorithms. To show an upper bound T(n) on the time complexity of a problem, one needs to show only that there is a particular algorithm with running time at most T(n). However, proving lower bounds is much more difficult, since lower bounds make a statement about all possible algorithms that solve a given problem. The phrase "all possible algorithms" includes not just the algorithms known today, but any algorithm that might be discovered in the future. To show a lower bound of T(n) for a problem requires showing that no algorithm can have time complexity lower than T(n). Upper and lower bounds are usually stated using the big O notation, which hides constant factors and smaller terms. This makes the bounds independent of the specific details of the computational model used. For instance, if T(n) = 7n2 + 15n + 40, in big O notation one would write T(n) = O(n2). Complexity classes Main article: Complexity class Defining complexity classes A complexity class is a set of problems of related complexity. Simpler complexity classes are defined by the following factors: The type of computational problem: The most commonly used problems are decision problems. However, complexity classes can be defined based on function problems, counting problems, optimization problems, promise problems, etc. The model of computation: The most common model of computation is the deterministic Turing machine, but many complexity classes are based on non-deterministic Turing machines, Boolean circuits, quantum Turing machines, monotone circuits, etc. The resource (or resources) that is being bounded and the bound: These two properties are usually stated together, such as "polynomial time", "logarithmic space", "constant depth", etc. Some complexity classes have complicated definitions that do not fit into this framework. Thus, a typical complexity class has a definition like the following: The set of decision problems solvable by a deterministic Turing machine within time f(n). (This complexity class is known as DTIME(f(n)).) But bounding the computation time above by some concrete function f(n) often yields complexity classes that depend on the chosen machine model. For instance, the language {xx | x is any binary string} can be solved in linear time on a multi-tape Turing machine, but necessarily requires quadratic time in the model of single-tape Turing machines. If we allow polynomial variations in running time, Cobham-Edmonds thesis states that "the time complexities in any two reasonable and general models of computation are polynomially related" (Goldreich 2008, Chapter 1.2). This forms the basis for the complexity class P, which is the set of decision problems solvable by a deterministic Turing machine within polynomial time. The corresponding set of function problems is FP. Important complexity classes A representation of the relation among complexity classes Many important complexity classes can be defined by bounding the time or space used by the algorithm. Some important complexity classes of decision problems defined in this manner are the following: Complexity class Model of computation Resource constraint Deterministic time DTIME(f(n)) Deterministic Turing machine Time O(f(n)) P Deterministic Turing machine Time O(poly(n)) EXPTIME Deterministic Turing machine Time O(2poly(n)) Non-deterministic time NTIME(f(n)) Non-deterministic Turing machine Time O(f(n)) NP Non-deterministic Turing machine Time O(poly(n)) NEXPTIME Non-deterministic Turing machine Time O(2poly(n)) Complexity class Model of computation Resource constraint Deterministic space DSPACE(f(n)) Deterministic Turing machine Space O(f(n)) L Deterministic Turing machine Space O(log n) PSPACE Deterministic Turing machine Space O(poly(n)) EXPSPACE Deterministic Turing machine Space O(2poly(n)) Non-deterministic space NSPACE(f(n)) Non-deterministic Turing machine Space O(f(n)) NL Non-deterministic Turing machine Space O(log n) NPSPACE Non-deterministic Turing machine Space O(poly(n)) NEXPSPACE Non-deterministic Turing machine Space O(2poly(n)) The logarithmic-space classes (necessarily) do not take into account the space needed to represent the problem. It turns out that PSPACE = NPSPACE and EXPSPACE = NEXPSPACE by Savitch's theorem. Other important complexity classes include BPP, ZPP and RP, which are defined using probabilistic Turing machines; AC and NC, which are defined using Boolean circuits; and BQP and QMA, which are defined using quantum Turing machines. #P is an important complexity class of counting problems (not decision problems). Classes like IP and AM are defined using Interactive proof systems. ALL is the class of all decision problems. Hierarchy theorems Main articles: time hierarchy theorem and space hierarchy theorem For the complexity classes defined in this way, it is desirable to prove that relaxing the requirements on (say) computation time indeed defines a bigger set of problems. In particular, although DTIME(n) is contained in DTIME(n2), it would be interesting to know if the inclusion is strict. For time and space requirements, the answer to such questions is given by the time and space hierarchy theorems respectively. They are called hierarchy theorems because they induce a proper hierarchy on the classes defined by constraining the respective resources. Thus there are pairs of complexity classes such that one is properly included in the other. Having deduced such proper set inclusions, we can proceed to make quantitative statements about how much more additional time or space is needed in order to increase the number of problems that can be solved. More precisely, the time hierarchy theorem states that {\displaystyle {\mathsf {DTIME}}{\big (}f(n){\big )}\subsetneq {\mathsf {DTIME}}{\big (}f(n)\cdot \log ^{2}(f(n)){\big )}}{\displaystyle {\mathsf {DTIME}}{\big (}f(n){\big )}\subsetneq {\mathsf {DTIME}}{\big (}f(n)\cdot \log ^{2}(f(n)){\big )}}. The space hierarchy theorem states

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