Cactus Language • Overview 3.2
• https://inquiryintoinquiry.com/2025/03/07/cactus-language-overview-3/

Given a body of conceivable propositions we need a way to follow the threads of their indications from their object domain to their values for the mind and a way to follow those same threads back again. Moreover, we need to implement both ways of proceeding in computational form. Thus we need programs for tracing the clues sentences provide from the universe of their objects to the signs of their values and, in turn, from signs to objects. Ultimately, we need to render propositions so functional as indicators of sets and so essential for examining the equality of sets as to give a rule for the practical conceivability of sets. Tackling that task requires us to introduce a number of new definitions and a collection of additional notational devices, to which we now turn.

Resources —

Cactus Language • Overview
• https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Overview

Survey of Animated Logical Graphs
• https://inquiryintoinquiry.com/2024/03/18/survey-of-animated-logical-graphs-7/

Survey of Theme One Program
• https://inquiryintoinquiry.com/2024/02/26/survey-of-theme-one-program-6/

#Peirce #Logic #Semiotics #LogicalGraphs #DifferentialLogic
#AutomataTheory #FormalLanguages #FormalGrammars #GraphTheory

Cactus Language • Overview 3.1
• https://inquiryintoinquiry.com/2025/03/07/cactus-language-overview-3/

In the development of Cactus Language to date the following two species of graphs have been instrumental.

• Painted And Rooted Cacti (PARCAI).
• Painted And Rooted Conifers (PARCOI).

It suffices to begin with the first class of data structures, developing their properties and uses in full, leaving discussion of the latter class to a part of the project where their distinctive features are key to developments at that stage. Partly because the two species are so closely related and partly for the sake of brevity, we'll always use the genus name “PARC” to denote the corresponding cacti.

To provide a computational middle ground between sentences seen as syntactic strings and propositions seen as indicator functions the language designer must not only supply a medium for the expression of propositions but also link the assertion of sentences to a means for inverting the indicator functions, that is, for computing the “fibers” or “inverse images” of the propositions.

#Peirce #Logic #Semiotics #LogicalGraphs #DifferentialLogic
#AutomataTheory #FormalLanguages #FormalGrammars #GraphTheory

Rabina Scott Finite Automat and Their Decision Problems

https://www.yodaiken.com/2025/01/30/rabina-scott-finite-automat-and-their-decision-problems/
#academics #theory #AutomataTheory #FiniteAutomate #Rabin #Scott #StateMachines

CC @lukego@twitter.com
#DrFill works by converting a crossword to a weighted csp, attempting to maximize the #probability that fill is correct
how good a z3 smt solver can be for this?
crossword with palindromes
In #automatatheory, eg a set of all palindromes in a given alphabet

In #automatatheory, a set of all palindromes in a given alphabet is a typical example of a language that is #contextfree, but not regular. This means that it is impossible for a computer with a finite amount of memory to reliably test for palindromes.

In #automatatheory, a set of all palindromes in a given alphabet is a typical example of a language that is #contextfree, but not regular. This means that it is impossible for a computer with a finite amount of memory to reliably test for palindromes.

Anyone have a good intro to #automata theory? Websites, articles, books, MOOCs, etc all welcome

Hashtag soup: #automatatheory #compsci #math

When theoreticians code:

/* The following table is intended to implement this DFA (in 'dot'
format). Note that 2 and 3 are "hidden" states used to step through
the possible out edges of state 1.

digraph html_filter {
0 -> 1 [label="<"];
0 -> 0;
1 -> 4 [label="'"];
1 -> 5 [label="\""];
1 -> 0 [label=">"];
1 -> 1;
4 -> 1 [label="'"];
4 -> 4;
5 -> 1 [label="\""];
5 -> 5;
}
*/

#automatatheory #codinglike1969