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Automatic generation of game content is an important challenge in computer game design. Such generation requires methods that are both efficient and guaranteed to produce playable content. While existing methods are adequate for currently available types of games, games based on more complex entities and structures may require new methods. In this paper, we use computational complexity analysis to...
Computational complexity is a branch of the theory of computation. It is used to measure how hard a problem is solved and the common measures include time and space. The classes of time complexity generally include: P, NP, NP-hard, NP-complete and EXPTIME; the classes of space complexity generally include: PSPACE, NPSPACE, PSPACE-hard and PSPACE-complete. Researching computational complexity of a...
We exhibit a deterministic concurrent reachability game PURGATORYn with n non-terminal positions and a binary choice for both players in every position so that any positional strategy for Player 1 achieving the value of the game within given isin < 1/2 must use non-zero behavior probabilities that are less than (isin2/(1 - isin))2n-2 . Also, even to achieve the value within say 1 - 2-n/2, doubly...
For several decades, the output from semiconductor manufacturers has been high volume products with process optimisation being continued throughout the lifetime of the product to ensure a satisfactory yield. However, product lifetimes are continually shrinking to keep pace with market demands. Furthermore there is an increase in dasiafoundrypsila business where product volumes are low; consequently...
In this paper, Level Set Method is introduced including its advantages and disadvantages. Then the key process of Particle Level Set Method is particularly introduced including particle initialization, particle re-distribution in normal direction of the interface, reduction of error, and particle reseeding. At last some typical Level Set examples of different grid numbers and some typical Particle...
A proxy signature enables an original signer to delegate her signing capability to a proxy signer and the proxy signer can sign a message on behalf of the original signer. Later, anyone accessible to the public keys of the original signer and proxy signer and the corresponding delegation warrant is able to verify the authenticity of a purported proxy signature. Obviously, the "public-verifiable"...
We define a propositional logic of games which lies in expressive power between the Propositional Dynamic Logic of Fischer and Ladner [FL] and the µ-calculus of Kozen [K]. We show that the logic is decidable and give a very simple, complete set of axioms, one of the rules being Brouwer's bar induction. Even though decidable, this logic is powerful enough to define well orderings. We state some other...
For each ε(0 ≤ ε ≪ 1) a family Gn =(V(Gn), E(Gn)) of a cyclic digraphs can be constructively defined having the following properties: (a) #V(Gn) ≤ n ?? 2n+2 (b) degree (Gn) ≤ constant (c) it is necessary to remove Ω(n ?? 2n) edges in order to reduce the depth of Gn to (2n)ε. It is then shown: For suitable constants c1, C2 ≫ 0, there are (fn, n)- grates (see Definition 1) of size linear in n, where...
Expanding graphs are the basic building blocks used in constructions of graphs with special connectivity properties such as superconcentrators. The only known explicit method (Margulis[7], Gabber and Galil[5]) of constructing arbitrarily large expanding graphs with a linear number of edges, uses graphs whose edges are defined by a finite set of linear mappings restricted to a two-dimensional set,...
This paper is an attempt at laying the foundations for the classification of queries on relational data bases according to their structure and their computational complexity. Using the operations of composition and fixpoints, a Σ-Π hierarchy of height, ω2, called the fixpoint query hierarchy, is defined, and its properties investigated. The hierarchy includes most of the queries considered in the...
We consider the game of Checkers generalized to an N × N board. Although certain properties of positions are efficiently computable (e.g., can Black jump all of White's pieces in a single move?), the general question, given a position, of whether a specified player can force a win against best play by his opponent, is shown to be PSPACE-hard. Under certain reasonable assumptions about the "drawing...
We define alternating Turing Machines which are like nondeterministic Turing Machines, except that existential and universal quantifiers alternate. Alternation links up time and space complexities rather well, in that alternating polynomial time equals deterministic polynomial space, and alternating linear space equals deterministic exponential time. Such considerations lead to a two-person game complete...
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