Mathematical Language Theory has become a rich field due to the seminal work of MIT's linguist, Noam Chomsky.

Briefly, the PHRASE STRUCTURE GRAMMAR of a SIMPLE SENTENCE EXAMPLE forms the TREE-GRAPH (a form studied elsewhere on this website under "TRAFGRAFS"):

			              [SENTENCE]
                                          /\
                                         /  \
                                        /    \
                                       /      \
                                      /        \
                                     /          \
                                    /            \
                            [SUBJECT]            [PREDICATE]
                               /\                     /\
                              /  \                   /  \
                             /    \                 /    \
                            /      \               /      \
                    [ARTICLE] [NOUN PHRASE][VERB PHRASE]  [OBJECT PHRASE]
                        |          /\            /\                  /\
                        |         /  \          /  \                /  \
                        |        /    \   [ADVERB] [VERB]          /    \
                        |       /      \       |       |          /      \
                        | [ADJECTIVE]  [NOUN]  |       |      [ARTICLE]  [NOUN]
                        |      |          |    |       |            |         |
                        |      |          |    |       |            |         |
                        |      |          |    |       |            |         |  
                       THE  SPOTTED      DOG  LOUDLY YELPED         A      GREETING.

Do you see how this can become a FLOWCHART FOR HOPPY TO TEACH HOPPY HOW TO HOP OUT A SENTENCE?

1. CREATE GRAMMAR TYPE-SETS with various MEMBERS (one or more of each SET TERMINATING THE TREE):
   • articles;
   • adjectives;
   • nouns;
   • adverbs;
   • verbs.
2. STARTING FROM "SENTENCE" POSITION, HOPPY HOPS DOWN A TREE-BRANCH TO A TERMINAL (RED);
3. HOPPY CALLS OUT THE TERMINAL TYPE (article or adjective or verb, etc.) TO THE CALCULATOR;
4. CALCULATOR RANDOMLY PICKS AN ITEM OF THE GIVEN GRAMMATICAL TYPE FROM A SET OF THEM;
5. HOPPY ANNOUNCES THE WORD TO PRINTER, WHICH PRINTS IT OUT.

---

FLOWCHART

                                    -----------
                                    \  START  /
                                     \       /
                                      \     /
                                       \   /
                                        \ /
                                         *
                                         |
                                         |
                                         v
                                         |
                                         |
             -------------->-------------*
            |                           / \                                 *
            |                          /   \                               / \
            ^                         /     \                             /   \
            |                        /       \        ______________     /     \        
       _____|______                 /TERMINAL?\-YES->-|ANNOUNCE TYPE|-->/LAST   \     
       |HOP AGAIN  |--<- NO---------\         /       ---------------  /TERMINAL?\
       ------------                  \       /    ___________          \         /   
                                      \     /-<---|HOP AGAIN|-<--NO-----\       /
                                       \   /      -----------            \     /
                                        \ /                               \   /
                                         *                                 \ /
                                                                            *
                                                                            |
                                                                           YES
                                                                            |
                                                                            V
                                                                           / \
                                                                          /   \
                                                                         /STOP \
                                                                         ------- 

CAN YOU SEE HOW TO CREATE TREE-GRAPHS FOR OTHER SENTENCE FORMS?

---

BONUS

CHOMSKY proved that EVERY TYPE OF PHRASE STRUCTURE GRAMMAR CORRESPONDENDED TO A PARTICULA TYPE OF FINITE STATE AUTOMATON ("machine" -- what I call a "logine", a device of FORMAL LANGUAGEUAGE).

A FINITE STATE AUTOMATON (a.k.a. FSA, a.k.a. COMPLETE SEQUENTIAL MACHINE) consists of:

1. A FINITE SET, I, OF INPUTS (homologous to GRAMMAR-TYPE MEMBERS);
2. A FINITE SET, S, OF INTERNAL STATES (homologous to GRAMMATICAL-TYPES);
3. A FINITE SET, O, OF OUTPUTS (homologous to words in sentence);
4. AN INITIAL STATE, S₀ (homologous to tree-root position, "SENTENCE");
5. A NEXT STATE FUNCTION, N (homologous to TREE-BRANCH);
6. AN OUTPUT FUNCTION, T (homologous to TERMINAL-BRAHCH), "ordering word selection".

Students in COMPUTER SCIENCE use these FSA in planning PROGRAMMING LANGUAGES or PROGRAMS.

Obviously, HOPPY could be taught to do this. (Can you help Hoppy?) In terminology used elsewhere at this Website -- as in the PECKING ORDER REPERTORY -- PHRASE STRUCTURE GRAMMARS and FINITE STATE AUTOMATONS are MEMBERS of a single REPERTORY: ABSTRACT FORMS (homologous to ACTORS IN REPERTORY COMPANY) which PEFORM DIFFERENT FUNCTIONS (homologous to different ROLES in plays) just by CHANGING LABELS (homologous to COSTUMES).