SymbolicTM
Symbolic Turing Machine for Busy Beaver problems
This program can be used to prove that a Turing Machine terminates or not by specifying a number of patterns with the use of regular expressions.
The Turing Machine is represented with the format use on bbchallenge.org followed by a empty line. An example is:
0 1
A 1RB 0RD
B 1LC 1LB
C 1RA 0LB
D 0RE 1RD
E --- 1RA
A rule consists of a state (named with a single capital starting with 'A') followed by a colong, a regular expression for the left side of the tape, the symbol (named with the digits starting with '0'), and a regular expression for the right side of the tape. In the regular expressions the '.' stand for any symbol, '+' for a repetition of one or more times of the sub expression to the left, '*' for a repetition zero or more times of the sub expression to the left, and '@' for an infinite repetition of the sub expression to the left. '(' and ')' can be used for grouping.
The program takes every pattern, applies one step of the Turing Machine to it, and verifies if the resulting pattern matches with one of the listed patterns. Depending on the direction a symbol is written to one tape and a symbol taken from the other tape. If the tape 'starts' (we assume that the left tape is reverted for this purpose of this description) of the form A+B, it is first rewritten as AAB before the first symbol is taken from A. If it is of the form AB, then it is also first rewritten to AA*B but also pattern where the first symbol is taken from B is verified. If the tape is of the form s@ it is rewritten as ss@.
Let L(E) stand for the language produced the regular expression E, than we say that A matches B if every string produced by L(A) is included in L(B). It is known that L(AA+) is equal to L(A+A) and that L(A*A) is equal to L(A+). The following rules apply:
- A matches .@
- A matches A
- A+ matches A*
- A+A matches A+
- AB matches CD if A matches C and B matches D
- A* matched B* if A matches B
- AB* matches C+ if A matches C and B matches C
- AB* matches C* if A matches C and B matches C
- AB+ matches C* if A matches C and B matches C