Using time-interval midpoints, discrete functions can approximate continuous or non-discrete functions {approximation by discrete function} {discrete function approximation}.
Ideal computers {non-deterministic computer} can choose better at decision points. Real computers {deterministic computer} choose by approximate methods.
Processing {non-linear processing} can describe quantity interactions. Multiplications combine two or more different measurable things to get new thing. Multiplication can reduce data from several quantities to one quantity. For example, gravitational force multiplies two interacting particle masses and then divides by distance between them. Multiplicative effects include division, differentiation, and integration. Differentiation reduces interaction number. Integration increases interaction number.
Analysis algorithms {forward analysis} can use assumptions about node relations to go from one node to another, to avoid costly and time-consuming backtracking.
Analysis algorithms {frame analysis} can use object-class variable, parameter, or property-type lists, with default values. However, such lists do not use "OR" relations well.
For hierarchies or networks, heuristic search methods {alpha-beta technique} {minimax algorithm} repeatedly evaluate nearby situations to check if they are nearer goal situation.
scoring
Alpha-beta technique assigns scores to all evaluated situations {node, hierarchy}. Score determines which nodes to check further.
node
Nodes have immediate-successor nodes. Alpha-beta technique checks beyond current nodes minimum distance and maximum distance {depth, search}. Node scores decide which immediate successors to check further. Alpha-beta technique removes low-scoring nodes {pruning} {alpha-beta pruning} or progressively worse nodes {tapered pruning}.
depth
Alpha-beta is depth first search, rather than width first. Alpha is maximum lower bound and can only increase. Beta is minimum upper bound and can only decrease.
Techniques {generate and test algorithm} for reaching goal situations can produce random or directed trials and check results.
Subtract searched-for message wavelet from possible wavelets to find wavelet that makes zero {Grover's algorithm} {Grover algorithm}. Invert wavelet. Probabilities stay the same. Find average amplitude. Invert wavelets around average amplitude. Searched-for wavelet magnifies amplitude while others reduce. Repeating converges on searched-for wavelet.
For hierarchical networks, searches {search, computer} {computer search} can go first to lower nodes {depth first search}, stay at same level {breadth first search}, or use evaluation function {heuristic search}|. Heuristic search tries to reach goal. It starts from current situation, evaluates nearby situations to short depth to see if goal is closer or farther, chooses only nearby situations that are closer, and then repeats, until exhausting all new nearby situations or finding goal.
evaluation
Evaluation uses scoring methods. Searching requires assigning probabilities. Search eliminates nodes by checking if they have successors, by assigning scores, or by checking for duplicates. Search can minimize risk {minimax, search}. Heuristic search can evaluate search steps to decide whether to go backward or forward {Shannon paradigm}. Search can use other strategies {set-of-support strategy} {unit preference strategy} {linear input form strategy} {ancestry-filtered strategy}.
Techniques {hill climbing}| for reaching goal situation can find path from initial to goal situation, while always maximizing score. Hill climbing locally improves answer until reaching optimum. Hill climbing often stops at solution that is not the best globally, because possible solutions are independent and are in different space locations, with valleys between them. Better hill climbing requires overview to check larger regions.
Techniques {hypothesize and match}| for reaching goal situation can make many examples to compare to true goal {match, search} or make and iteratively test better hypotheses until one matches.
For reaching goal situations, techniques {resolution procedure}| {resolution principle} can check if all formulas are true and check if negative of formula to prove is unsatisfiable, to imply formula. Resolution procedures work if formulas, expressed in predicate calculus, describe situation space. Formulas must allow causality, ability, temporality, recursion formulas, and spatial relations.
Problems can have initial situations, possible situations, actions moving from one situation to another, action relations, and goal situations {situation space}|. Solving problem involves finding path from initial situation to goal situation, while avoiding traps.
Techniques {system inference model} for reaching goal situations can find function or relation between initial situation and goal situation or build relations using examples and counterexamples.
3-Computer Science-Software-Algorithm
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Date Modified: 2022.0225