Logic: New Applications
https://www.maplesoft.com/applications/category.aspx?cid=145
en-us2022 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemThu, 20 Jan 2022 18:00:06 GMTThu, 20 Jan 2022 18:00:06 GMTNew applications in the Logic categoryhttps://www.maplesoft.com/images/Application_center_hp.jpgLogic: New Applications
https://www.maplesoft.com/applications/category.aspx?cid=145
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 BrightPolynomizing Lukasiewicz's Many-Valued Logics by Maple
https://www.maplesoft.com/applications/view.aspx?SID=154488&ref=Feed
Maple Procedures are presented to express propositions and connectives of propositional Lukasiewicz's n-valued logic for n≤4 in terms of certain polynomials. Evaluations and checking of tautologies are done by procedures based on Groebner’s bases.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Polynomizing Lukasiewicz's Many-Valued Logics by Maple" style="max-width: 25%;" align="left"/>Maple Procedures are presented to express propositions and connectives of propositional Lukasiewicz's n-valued logic for n≤4 in terms of certain polynomials. Evaluations and checking of tautologies are done by procedures based on Groebner’s bases.https://www.maplesoft.com/applications/view.aspx?SID=154488&ref=FeedMon, 10 Sep 2018 04:00:00 ZKahtan H. AlzubaidyKahtan H. AlzubaidyLukasiewicz's Many-Valued Logic - Arithmetic Semantic
https://www.maplesoft.com/applications/view.aspx?SID=154466&ref=Feed
Maple Procedures are presented to evaluate propositions and to check tautologies in Lukasiewicz's n-valued logic. Atomic propositions are represented by numerical variables and logical connectives by suitable functions. Evaluations and checking are done for compound propositions consisting of at most four atomic propositions.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Lukasiewicz's Many-Valued Logic - Arithmetic Semantic" style="max-width: 25%;" align="left"/>Maple Procedures are presented to evaluate propositions and to check tautologies in Lukasiewicz's n-valued logic. Atomic propositions are represented by numerical variables and logical connectives by suitable functions. Evaluations and checking are done for compound propositions consisting of at most four atomic propositions.https://www.maplesoft.com/applications/view.aspx?SID=154466&ref=FeedSat, 09 Jun 2018 04:00:00 ZKahtan H. AlzubaidyKahtan H. AlzubaidyFuzzy Sets in Examples
https://www.maplesoft.com/applications/view.aspx?SID=141714&ref=Feed
<p>This worksheet has been created first as a practical part of short course on the pattern recognition theory for my students. It had intended to their introduce, including visually impressions, with fuzzy sets and basic rules of simple operations with them. MAPLE tools were extremely comfortable for such a task and this experience may be useful for community colleagues.</p><img src="https://www.maplesoft.com/view.aspx?si=141714/fuzzy-sets.jpg" alt="Fuzzy Sets in Examples" style="max-width: 25%;" align="left"/><p>This worksheet has been created first as a practical part of short course on the pattern recognition theory for my students. It had intended to their introduce, including visually impressions, with fuzzy sets and basic rules of simple operations with them. MAPLE tools were extremely comfortable for such a task and this experience may be useful for community colleagues.</p>https://www.maplesoft.com/applications/view.aspx?SID=141714&ref=FeedSat, 22 Dec 2012 05:00:00 ZProf. Gennady P. ChuikoProf. Gennady P. ChuikoMathematical Logic. Guidelines. Maple vs. MS Words.
https://www.maplesoft.com/applications/view.aspx?SID=102213&ref=Feed
<p>Maple vs. MS Words. Example<br />It is interesting to someone interested in it?<br />For me it is obvious that the best books and teaching materials of classical mathematics must be formatted in mathematical packages.</p><img src="https://www.maplesoft.com/view.aspx?si=102213/mrs.jpg" alt="Mathematical Logic. Guidelines. Maple vs. MS Words." style="max-width: 25%;" align="left"/><p>Maple vs. MS Words. Example<br />It is interesting to someone interested in it?<br />For me it is obvious that the best books and teaching materials of classical mathematics must be formatted in mathematical packages.</p>https://www.maplesoft.com/applications/view.aspx?SID=102213&ref=FeedFri, 04 Mar 2011 05:00:00 ZDonetsk National UniversityDonetsk National UniversityFuzzySets
https://www.maplesoft.com/applications/view.aspx?SID=96899&ref=Feed
<p>FuzzySets for Maple™ is an easy-to-use toolbox for Maple which allows professionals, researchers, and students to learn about, experiment with, and model systems through fuzzy logic and fuzzy sets in the Maple worksheet environment. It transforms Maple into a system which works with fuzzy values and fuzzy sets as seamlessly as the basic system deals with classical logic and sets. The functionality includes most principal areas of fuzzy logic and fuzzy sets, including fuzzy control theory.</p><img src="https://www.maplesoft.com/view.aspx?si=96899/FuzzySets_logosm.gif" alt="FuzzySets" style="max-width: 25%;" align="left"/><p>FuzzySets for Maple™ is an easy-to-use toolbox for Maple which allows professionals, researchers, and students to learn about, experiment with, and model systems through fuzzy logic and fuzzy sets in the Maple worksheet environment. It transforms Maple into a system which works with fuzzy values and fuzzy sets as seamlessly as the basic system deals with classical logic and sets. The functionality includes most principal areas of fuzzy logic and fuzzy sets, including fuzzy control theory.</p>https://www.maplesoft.com/applications/view.aspx?SID=96899&ref=FeedWed, 15 Sep 2010 04:00:00 ZDouglas HarderDouglas HarderFinding 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 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 HarderIntroduction 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 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 Harder