CoCalc -- Func.h

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A (one dimensional) cellular automaton is a function1 F : Σ → Σ with the property that there is a K > 0 such that F (x)i depends only on the 2K + 1 coordinates xi−K , xi−K+1, . . . , xi−1, xi, xi+1, . . . , xi+K . A periodic point of σ is any x such that σ^p (x) = x for some p ∈ N, and a periodic point of F is any x such that F^q (x) = x for some q ∈ N. Given a cellular automaton F, a point x ∈ Σ is jointly periodic if there are p, q ∈ N such that σ^p (x) = F^q (x) = x, that is, it is a periodic point under both functions.

This project aims to explore the nature of one-dimensional Cellular Automata, in the hope of finding the structure of cellular automata through its periodic points.

Shared Project -- M498ES23-Cellular-Automata

LEMMA Research Project / Code / Source code / Program (1) / Program / Source / Func.h

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License: MIT
ubuntu2004

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/*
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 * Copyright (C) 2004 Bryant Lee
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 *
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 * This file is part of FPeriod.
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 *
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 * FPeriod is free software; you can redistribute it and/or modify
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 * it under the terms of the GNU General Public License as published by
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 * the Free Software Foundation; either version 2 of the License, or
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 * (at your option) any later version.
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 *
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 * FPeriod is distributed in the hope that it will be useful,
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 * but WITHOUT ANY WARRANTY; without even the implied warranty of
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 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
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 * GNU General Public License for more details.
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 *
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 * You should have received a copy of the GNU General Public License
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 * along with FPeriod; if not, write to the Free Software
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 * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
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 */
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/**
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 * Represents a polynomial function in terms x[-s,t] mod N
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 *
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 * Written by: Bryant Lee
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 * Date: 10/31/04
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 **/
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#ifndef FUNC_H
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#define FUNC_H
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#include "FuncNode.h"
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#include <fstream> //for printing
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#include <string>
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#include <list>
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#include <vector>
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#include <map> //actually used only for opt polynomials
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#include "StorageKey.h" //used only for opt polynomials lookup map
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class Func {
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 private:
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  string str;
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  list<FuncNode*> fList; //list representation of function (poly repres.)
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  int* fTable; //lookup representation of function (table repres.)
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  int shiftSize; //#symbols in shift
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  int type; //0 = table, 1 = polynomial, 2= optimized polynomial
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  unsigned int span; //span (table repres. only)
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  unsigned int tablesize; //(table repres. only)
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  //-- member vars used for OPT functions ONLY
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  vector<int> optTerms;
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  map<StorageKey, byte> optLookupMap; //takes a vector of term values, returns answer
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  map<int, int> optFindTerm; //key = term #, val = coord in "compact" array
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  //--
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  //generates the index-th term of the image of x
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  byte timage(byte *word, int wordLength, int index);
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  unsigned int timage(unsigned int * word, int wordLength, int index);
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  // (used in opt polynomial functions only: for precomputing to lookup table)
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  // generates value of function based on inputs
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  byte timage_by_inputs(byte *inTerms, int numTerms,
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			const map<int,int> &optFindTerm);
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 public:
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  //constructor
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  Func(const string & iStr, int iShiftSize, bool opt);
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  //destructor
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  ~Func();
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  //print
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  void print(ofstream & fout);
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  //return image of word x
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  void image(byte *word, int wordLength, byte *output);
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  //return image of word x
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  void image(unsigned int * word, int wordLength, unsigned int *output,
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	     unsigned int blocks);
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  //return true if this is an opt polynomial function
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  bool isOpt();
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};
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#endif
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