Logic: New Applications
https://www.maplesoft.com/applications/category.aspx?cid=206
en-us2021 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemFri, 22 Jan 2021 07:12:16 GMTFri, 22 Jan 2021 07:12:16 GMTNew applications in the Logic categoryhttps://www.maplesoft.com/images/Application_center_hp.jpgLogic: New Applications
https://www.maplesoft.com/applications/category.aspx?cid=206
Graph Colouring with SAT
https://www.maplesoft.com/applications/view.aspx?SID=154550&ref=Feed
A colouring of a graph is an assignment of colours to its vertices such that every two adjacent vertices are coloured differently. Finding a colouring of a given graph using the fewest number of colours is a difficult problem in general. In this worksheet we demonstrate how to solve the graph colouring problem by translating it into Boolean logic and using Maple's built-in efficient SAT solver. This approach is now available as an option to Maple’s ChromaticNumber function, which also solves the graph colouring problem. Using SAT can dramatically improve the performance of this function in some cases, including the “queen graphs” problem shown in this application.<img src="https://www.maplesoft.com/view.aspx?si=154550/queens_colouring.png" alt="Graph Colouring with SAT" style="max-width: 25%;" align="left"/>A colouring of a graph is an assignment of colours to its vertices such that every two adjacent vertices are coloured differently. Finding a colouring of a given graph using the fewest number of colours is a difficult problem in general. In this worksheet we demonstrate how to solve the graph colouring problem by translating it into Boolean logic and using Maple's built-in efficient SAT solver. This approach is now available as an option to Maple’s ChromaticNumber function, which also solves the graph colouring problem. Using SAT can dramatically improve the performance of this function in some cases, including the “queen graphs” problem shown in this application.https://www.maplesoft.com/applications/view.aspx?SID=154550&ref=FeedMon, 09 Sep 2019 04:00:00 ZCurtis BrightCurtis BrightSolving the 15-puzzle
https://www.maplesoft.com/applications/view.aspx?SID=154509&ref=Feed
The 15-puzzle is a classic "sliding tile" puzzle that consists of tiles arranged in a 4 by 4 grid with one tile missing. The objective is to arrange the tiles in a sorted order only by making moves that slide a tile into the empty space. In this worksheet we demonstrate how this puzzle can be solved by encoding its rules into Boolean logic and using Maple's SAT solver.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Solving the 15-puzzle" style="max-width: 25%;" align="left"/>The 15-puzzle is a classic "sliding tile" puzzle that consists of tiles arranged in a 4 by 4 grid with one tile missing. The objective is to arrange the tiles in a sorted order only by making moves that slide a tile into the empty space. In this worksheet we demonstrate how this puzzle can be solved by encoding its rules into Boolean logic and using Maple's SAT solver.https://www.maplesoft.com/applications/view.aspx?SID=154509&ref=FeedWed, 19 Dec 2018 05:00:00 ZCurtis BrightCurtis BrightInteractive Sudoku
https://www.maplesoft.com/applications/view.aspx?SID=154507&ref=Feed
This worksheet contains an interactive Sudoku game that allows one to play a game of Sudoku in Maple. New puzzles can be randomly generated, read from a file, or loaded an online source, and puzzles can be automatically solved.
No knowledge of Sudoku solving or puzzle generation was used in the implementation. Instead, the rules of Sudoku were encoded into Boolean logic and Maple's built-in SAT solver was used; source code and implementation details are included.<img src="https://www.maplesoft.com/view.aspx?si=154507/suduko.png" alt="Interactive Sudoku" style="max-width: 25%;" align="left"/>This worksheet contains an interactive Sudoku game that allows one to play a game of Sudoku in Maple. New puzzles can be randomly generated, read from a file, or loaded an online source, and puzzles can be automatically solved.
No knowledge of Sudoku solving or puzzle generation was used in the implementation. Instead, the rules of Sudoku were encoded into Boolean logic and Maple's built-in SAT solver was used; source code and implementation details are included.https://www.maplesoft.com/applications/view.aspx?SID=154507&ref=FeedMon, 03 Dec 2018 05:00:00 ZCurtis BrightCurtis BrightClique Finding with SAT
https://www.maplesoft.com/applications/view.aspx?SID=154502&ref=Feed
A clique of a graph is a subset of its vertices that are all mutually connected. Finding a clique of a given size in a graph is a difficult problem in general.
In this worksheet we demonstrate how to solve the clique finding problem by translating it into Boolean logic and using Maple's built-in efficient SAT solver. This approach even can out-perform the built-in Maple function FindClique which also solves the clique finding problem.<img src="https://www.maplesoft.com/view.aspx?si=154502/graph20.png" alt="Clique Finding with SAT" style="max-width: 25%;" align="left"/>A clique of a graph is a subset of its vertices that are all mutually connected. Finding a clique of a given size in a graph is a difficult problem in general.
In this worksheet we demonstrate how to solve the clique finding problem by translating it into Boolean logic and using Maple's built-in efficient SAT solver. This approach even can out-perform the built-in Maple function FindClique which also solves the clique finding problem.https://www.maplesoft.com/applications/view.aspx?SID=154502&ref=FeedThu, 15 Nov 2018 05:00:00 ZCurtis BrightCurtis BrightFinding Graeco-Latin Squares
https://www.maplesoft.com/applications/view.aspx?SID=154499&ref=Feed
A Latin square is an n by n arrangement of n items such that each item appears exactly once in each row and column. A Graeco-Latin square is a pair of two Latin squares such that all n^2 pairs of the items arise when one square is superimposed onto the other.
In this worksheet we use Maple's built-in efficient SAT solver to find Graeco-Latin squares without using any knowledge of search algorithms or construction methods.<img src="https://www.maplesoft.com/view.aspx?si=154499/Graeco-Latin-10.png" alt="Finding Graeco-Latin Squares" style="max-width: 25%;" align="left"/>A Latin square is an n by n arrangement of n items such that each item appears exactly once in each row and column. A Graeco-Latin square is a pair of two Latin squares such that all n^2 pairs of the items arise when one square is superimposed onto the other.
In this worksheet we use Maple's built-in efficient SAT solver to find Graeco-Latin squares without using any knowledge of search algorithms or construction methods.https://www.maplesoft.com/applications/view.aspx?SID=154499&ref=FeedWed, 07 Nov 2018 05:00:00 ZCurtis BrightCurtis BrightSolving the World's Hardest Sudoku
https://www.maplesoft.com/applications/view.aspx?SID=154483&ref=Feed
Sudoku is a popular puzzle that appears in many puzzle books and newspapers. We can use Maple's built-in efficient SAT solver to quickly solve the "world's hardest Sudoku" without any knowledge of Sudoku solving techniques.<img src="https://www.maplesoft.com/view.aspx?si=154483/72f8a9282f0b80d9423ca565563bb9d6.gif" alt="Solving the World's Hardest Sudoku" style="max-width: 25%;" align="left"/>Sudoku is a popular puzzle that appears in many puzzle books and newspapers. We can use Maple's built-in efficient SAT solver to quickly solve the "world's hardest Sudoku" without any knowledge of Sudoku solving techniques.https://www.maplesoft.com/applications/view.aspx?SID=154483&ref=FeedThu, 04 Oct 2018 04:00:00 ZCurtis BrightCurtis BrightThe n-Queens Problem
https://www.maplesoft.com/applications/view.aspx?SID=154482&ref=Feed
The n-Queens problem is to place n queens on an n by n chessboard such that no two queens are mutually attacking. We can use Maple's built-in efficient SAT solver to quickly solve this problem.<img src="https://www.maplesoft.com/view.aspx?si=154482/nQueens.PNG" alt="The n-Queens Problem" style="max-width: 25%;" align="left"/>The n-Queens problem is to place n queens on an n by n chessboard such that no two queens are mutually attacking. We can use Maple's built-in efficient SAT solver to quickly solve this problem.https://www.maplesoft.com/applications/view.aspx?SID=154482&ref=FeedThu, 04 Oct 2018 04:00:00 ZCurtis BrightCurtis BrightSolving the Einstein Riddle
https://www.maplesoft.com/applications/view.aspx?SID=154484&ref=Feed
The "Einstein Riddle" is a logic puzzle apocryphally attributed to Albert Einstein and is often stated with the remark that it is only solvable by 2% of the world's population. We can solve this puzzle using Maple's built-in efficient SAT solver.<img src="https://www.maplesoft.com/view.aspx?si=154484/Einstein_Riddle.jpg" alt="Solving the Einstein Riddle" style="max-width: 25%;" align="left"/>The "Einstein Riddle" is a logic puzzle apocryphally attributed to Albert Einstein and is often stated with the remark that it is only solvable by 2% of the world's population. We can solve this puzzle using Maple's built-in efficient SAT solver.https://www.maplesoft.com/applications/view.aspx?SID=154484&ref=FeedThu, 04 Oct 2018 04:00:00 ZCurtis BrightCurtis BrightFinding Minimal Sum for Boolean Expression
https://www.maplesoft.com/applications/view.aspx?SID=5086&ref=Feed
Worksheet which provides methods for minimizing boolean expressions. Example usage is provided.<img src="https://www.maplesoft.com/view.aspx?si=5086//applications/images/app_image_blank_lg.jpg" alt="Finding Minimal Sum for Boolean Expression" style="max-width: 25%;" align="left"/>Worksheet which provides methods for minimizing boolean expressions. Example usage is provided.https://www.maplesoft.com/applications/view.aspx?SID=5086&ref=FeedWed, 11 Jul 2007 00:00:00 ZJay PedersenJay PedersenPrime Implicants of Boolean Expression by Concensus method
https://www.maplesoft.com/applications/view.aspx?SID=4970&ref=Feed
Determines prime implicants of boolean expressions using the Consensus method. This is used in simplification of boolean expressions.<img src="https://www.maplesoft.com/view.aspx?si=4970//applications/images/app_image_blank_lg.jpg" alt="Prime Implicants of Boolean Expression by Concensus method" style="max-width: 25%;" align="left"/>Determines prime implicants of boolean expressions using the Consensus method. This is used in simplification of boolean expressions.https://www.maplesoft.com/applications/view.aspx?SID=4970&ref=FeedTue, 29 May 2007 00:00:00 ZJay PedersenJay PedersenIntroduction to Fuzzy Controllers
https://www.maplesoft.com/applications/view.aspx?SID=1398&ref=Feed
This worksheet uses FuzzySets for Maple to demonstrate several examples solving fuzzy logic problems in Maple.<img src="https://www.maplesoft.com/view.aspx?si=1398/FuzzySets_logo.gif" alt="Introduction to Fuzzy Controllers" style="max-width: 25%;" align="left"/>This worksheet uses FuzzySets for Maple to demonstrate several examples solving fuzzy logic problems in Maple.https://www.maplesoft.com/applications/view.aspx?SID=1398&ref=FeedMon, 01 Nov 2004 00:00:00 ZDouglas HarderDouglas HarderMathematical Introduction to Fuzzy Logic, Fuzzy Sets, and Fuzzy Controls
https://www.maplesoft.com/applications/view.aspx?SID=1409&ref=Feed
Classical logic is based on binary logic with two values of truth. In Maple, these two values are true and false .
Fuzzy logic is a multivalued logic with truth represented by a value on the closed interval [0, 1], where 0 is equated with the classical false value and 1 is equated with the classical true value. Values in (0, 1) indicate varying degrees of truth.
For example, the question Is that person over 180 cm feet tall? has only two answers, yes or no .
On the other hand, the question Is that person tall? has many answers. Someone over 190 cm is almost universally considered to be tall. Someone who is 180 cm may be considered to be sort of tall , while someone who is under 160 cm is not usually considered to be tall.<img src="https://www.maplesoft.com/view.aspx?si=1409/FuzzySets_logo.gif" alt="Mathematical Introduction to Fuzzy Logic, Fuzzy Sets, and Fuzzy Controls" style="max-width: 25%;" align="left"/>Classical logic is based on binary logic with two values of truth. In Maple, these two values are true and false .
Fuzzy logic is a multivalued logic with truth represented by a value on the closed interval [0, 1], where 0 is equated with the classical false value and 1 is equated with the classical true value. Values in (0, 1) indicate varying degrees of truth.
For example, the question Is that person over 180 cm feet tall? has only two answers, yes or no .
On the other hand, the question Is that person tall? has many answers. Someone over 190 cm is almost universally considered to be tall. Someone who is 180 cm may be considered to be sort of tall , while someone who is under 160 cm is not usually considered to be tall.https://www.maplesoft.com/applications/view.aspx?SID=1409&ref=FeedMon, 01 Nov 2004 00:00:00 ZDouglas HarderDouglas HarderIntroduction to Fuzzy Sets on a Real Domain
https://www.maplesoft.com/applications/view.aspx?SID=1410&ref=Feed
The RealDomain subpackage of FuzzySets allows the user to construct and work with fuzzy subsets of the real line.
The membership function of a fuzzy subset of the real line is represented by a piecewise function with a range of [0, 1].
The RealDomain subpackage includes a number of constructors of fuzzy subsets of R which simplify the construction of fuzzy sets and set operators and routines for working with fuzzy subsets of R .<img src="https://www.maplesoft.com/view.aspx?si=1410/FuzzySets_logo.gif" alt="Introduction to Fuzzy Sets on a Real Domain" style="max-width: 25%;" align="left"/>The RealDomain subpackage of FuzzySets allows the user to construct and work with fuzzy subsets of the real line.
The membership function of a fuzzy subset of the real line is represented by a piecewise function with a range of [0, 1].
The RealDomain subpackage includes a number of constructors of fuzzy subsets of R which simplify the construction of fuzzy sets and set operators and routines for working with fuzzy subsets of R .https://www.maplesoft.com/applications/view.aspx?SID=1410&ref=FeedMon, 01 Nov 2004 00:00:00 ZDouglas HarderDouglas HarderEnumerating All Subsets of a Set
https://www.maplesoft.com/applications/view.aspx?SID=4244&ref=Feed
This worksheet enumerates all subsets of a given set and computes the sum of each subset.
Lists are used instead of sets below, because order of the elements in a set is crucial in order to list all subsets without repetition.<img src="https://www.maplesoft.com/view.aspx?si=4244//applications/images/app_image_blank_lg.jpg" alt="Enumerating All Subsets of a Set " style="max-width: 25%;" align="left"/>This worksheet enumerates all subsets of a given set and computes the sum of each subset.
Lists are used instead of sets below, because order of the elements in a set is crucial in order to list all subsets without repetition.https://www.maplesoft.com/applications/view.aspx?SID=4244&ref=FeedThu, 21 Mar 2002 14:42:34 ZYufang HaoYufang HaoMastermind maplet
https://www.maplesoft.com/applications/view.aspx?SID=4220&ref=Feed
This maplet simulates the classic board game Mastermind (TM)<img src="https://www.maplesoft.com/view.aspx?si=4220/appviewer.aspx.jpg" alt="Mastermind maplet" style="max-width: 25%;" align="left"/>This maplet simulates the classic board game Mastermind (TM)https://www.maplesoft.com/applications/view.aspx?SID=4220&ref=FeedThu, 24 Jan 2002 13:20:24 ZDouglas HarderDouglas HarderLogic and truth tables
https://www.maplesoft.com/applications/view.aspx?SID=4095&ref=Feed
We're going to use Maple to create truth tables for logical expressions. To do this we are going to define some custom built functions. <img src="https://www.maplesoft.com/view.aspx?si=4095//applications/images/app_image_blank_lg.jpg" alt="Logic and truth tables " style="max-width: 25%;" align="left"/>We're going to use Maple to create truth tables for logical expressions. To do this we are going to define some custom built functions. https://www.maplesoft.com/applications/view.aspx?SID=4095&ref=FeedFri, 17 Aug 2001 13:23:51 ZGregory MooreGregory MooreFuzzy controler for reversed pendulum
https://www.maplesoft.com/applications/view.aspx?SID=3928&ref=Feed
Given an initial state for an unstable nonlinear mechanical system of the reversed pendulum, the purpose is to find a sequence of forces to adjust the system to be in a stable state by inference rules of fuzzy logic.<img src="https://www.maplesoft.com/view.aspx?si=3928//applications/images/app_image_blank_lg.jpg" alt="Fuzzy controler for reversed pendulum " style="max-width: 25%;" align="left"/>Given an initial state for an unstable nonlinear mechanical system of the reversed pendulum, the purpose is to find a sequence of forces to adjust the system to be in a stable state by inference rules of fuzzy logic.https://www.maplesoft.com/applications/view.aspx?SID=3928&ref=FeedTue, 10 Jul 2001 11:17:25 ZDr. Laczik BálintDr. Laczik BálintSolving constraint satisfaction problems III: Paint by numbers
https://www.maplesoft.com/applications/view.aspx?SID=3510&ref=Feed
We can generalize the technique of interacting copies to write a single procedure to handle a whole class of puzzles. These puzzles are known as Paint-by-Numbers, and also as Nonograms, or O-e-kaki in Japanese. We are given a rectangular grid of pixels. For each row and column, we are told the lengths of the groups of pixels that are black in that row or column. The challenge is to use that information to figure put the exact placement of the pixels.<img src="https://www.maplesoft.com/view.aspx?si=3510/paint.gif" alt="Solving constraint satisfaction problems III: Paint by numbers" style="max-width: 25%;" align="left"/>We can generalize the technique of interacting copies to write a single procedure to handle a whole class of puzzles. These puzzles are known as Paint-by-Numbers, and also as Nonograms, or O-e-kaki in Japanese. We are given a rectangular grid of pixels. For each row and column, we are told the lengths of the groups of pixels that are black in that row or column. The challenge is to use that information to figure put the exact placement of the pixels.https://www.maplesoft.com/applications/view.aspx?SID=3510&ref=FeedMon, 18 Jun 2001 00:00:00 ZCarl DeVoreCarl DeVoreSolving constraint satisfaction problems II: More difficult logic problems
https://www.maplesoft.com/applications/view.aspx?SID=3509&ref=Feed
This application uses a Maple package called LP that solves word logic problems such as, identify the people around a table given a list of clues about their relationships.<img src="https://www.maplesoft.com/view.aspx?si=3509//applications/images/app_image_blank_lg.jpg" alt="Solving constraint satisfaction problems II: More difficult logic problems" style="max-width: 25%;" align="left"/>This application uses a Maple package called LP that solves word logic problems such as, identify the people around a table given a list of clues about their relationships.https://www.maplesoft.com/applications/view.aspx?SID=3509&ref=FeedMon, 18 Jun 2001 00:00:00 ZCarl DeVoreCarl DeVoreSolving constraint satisfaction problems IV: Combinatorial square coloring
https://www.maplesoft.com/applications/view.aspx?SID=3511&ref=Feed
Beverly has a pigeonhole shelf with 36 square holes in a 6x6 grid. She keeps a minature fork, knife, or spoon in each hole such that in each row and column there are exactly two of each. The goal is to deduce the placement of each.<img src="https://www.maplesoft.com/view.aspx?si=3511/pigeon.gif" alt="Solving constraint satisfaction problems IV: Combinatorial square coloring" style="max-width: 25%;" align="left"/>Beverly has a pigeonhole shelf with 36 square holes in a 6x6 grid. She keeps a minature fork, knife, or spoon in each hole such that in each row and column there are exactly two of each. The goal is to deduce the placement of each.https://www.maplesoft.com/applications/view.aspx?SID=3511&ref=FeedMon, 18 Jun 2001 00:00:00 ZCarl DeVoreCarl DeVore