diff options
Diffstat (limited to 'entries/jj/tm/fib-desc.txt')
| -rw-r--r-- | entries/jj/tm/fib-desc.txt | 98 |
1 files changed, 52 insertions, 46 deletions
diff --git a/entries/jj/tm/fib-desc.txt b/entries/jj/tm/fib-desc.txt index c766da6..b98b324 100644 --- a/entries/jj/tm/fib-desc.txt +++ b/entries/jj/tm/fib-desc.txt @@ -11,14 +11,15 @@ A Turing machine is a 7-tuple T = (Q,Σ,Γ,δ,qI,qA,qR) where: - qR ∈ Q is the reject state - Q: { + ca, cb, cc, cd, ce, cf, cg, ch, ci, sa, sb, sc, sd, aa, ab, ac, aaa, aab, aac, aad, aae, aaf, - aba, abb, abc, abd, abe, abf, abg, abh, + aba, abb, abc, abd, abe, abf, ba, bb, bc, baa, bab, bac, bad, bae, baf, bba, bbb, bbc, bbd, bbe, bbf, - ca, cb, cc, cd, ce, cf, cg, ch, ci + za, zb, zc, zd } - Σ: not relevant as we entirely disregard the input to begin with. - Γ: {_, $, X, 0, 1, 0*, 1*} (_ means the blank symbol) @@ -43,7 +44,7 @@ states c*: clearing the initial tape δ(ca, Γ) -> (cb, $, R) δ(cb, Γ) -> (cc, 0, R) δ(cc, Γ) -> (cd, $, R) -δ(cd, Γ) -> (ce, 1, R) +δ(cd, Γ) -> (ce, 1*, R) δ(ce, Γ) -> (cf, $, R) δ(cf, Γ) -> (cg, 1, R) δ(cg, Γ) -> (ch, $, R) @@ -54,10 +55,10 @@ states c*: clearing the initial tape states s*: making space for the next number - from the end: append XX...X where len(XX...X) = len(previous_number) -δ(sa, Γ \ $) -> (sa, , L) +δ(sa, {_,X}) -> (sa, , L) δ(sa, $) -> (sb, , L) -δ(sb, Γ \ {0,1,$}) -> (sb, , L) +δ(sb, {0*,1*}) -> (sb, , L) δ(sb, 0) -> (sc, 0*, R) δ(sb, 1) -> (sc, 1*, R) δ(sb, $) -> (sd, , R) @@ -65,7 +66,7 @@ states s*: making space for the next number δ(sc, Γ \ _) -> (sc, , R) δ(sc, _) -> (sa, X, L) -δ(sd, Γ \ {0*,1*,_}) -> (sd, , R) +δ(sd, {$,X}) -> (sd, , R) δ(sd, 0*) -> (sd, 0, R) δ(sd, 1*) -> (sd, 1, R) δ(sd, _) -> (aa, , L) @@ -77,11 +78,11 @@ states a*: add the last digit of both numbers without carrying - 1: replace with 1*, goto state (aba) - $: do not replace, read right until _, write $, goto state (s) -δ(aa, Γ \ $) -> (aa, , L) +δ(aa, {X,0,1}) -> (aa, , L) δ(aa, $) -> (ab, , L) +δ(ab, {0*,1*}) -> (ab, , L) δ(ab, 0) -> (aaa, 0*, L) - δ(ab, 1) -> (aba, 1*, L) δ(ab, $) -> (ac, , R) @@ -93,20 +94,22 @@ states aa* - 0*: replace with 0, read right until _, then read left until X and replace with 0 - 1*: replace with 1, read right until _, then read left until X and replace with 1 -δ(aaa, Γ \ $) -> (aaa, , L) +δ(aaa, {0,1}) -> (aaa, , L) δ(aaa, $) -> (aab, , L) δ(aab, 0*) -> (aac, 0, R) δ(aac, Γ \ _) -> (aac, , R) δ(aac, _) -> (aad, , L) -δ(aad, Γ \ X) -> (aad, , L) -δ(aad, X) -> (aba, 0, L) +δ(aad, {0,1}) -> (aad, , L) +δ(aad, X) -> (aa, 0, L) -δ(aab, 1*) -> (aad, 1, R) +δ(aab, 1*) -> (aae, 1, R) δ(aae, Γ \ _) -> (aae, , R) δ(aae, _) -> (aaf, , L) -δ(aaf, Γ \ X) -> (aaf, , L) -δ(aaf, X) -> (baa, 1, L) +δ(aaf, {0,1}) -> (aaf, , L) +δ(aaf, X) -> (aa, 1, L) + +δ(aab, {0,1}) -> (aab, , L) states ab* - read left until $, then read left until: @@ -114,100 +117,103 @@ states ab* - $: do not replace, read right until _, then read left until X and replace with 1 - 1*: replace with 1, read right until _, then read left until X and replace with 0, goto state (b) -δ(aba, Γ \ $) -> (aba, , L) +δ(aba, {0,1}) -> (aba, , L) δ(aba, $) -> (abb, , L) δ(abb, 0*) -> (abc, 0, R) δ(abc, Γ \ _) -> (abc, , R) δ(abc, _) -> (abd, , L) -δ(abd, Γ \ X) -> (abd, , L) +δ(abd, {0,1}) -> (abd, , L) δ(abd, X) -> (aa, 1, L) -δ(abb, $) -> (abe, , R) +δ(abb, 1*) -> (abe, 1, R) δ(abe, Γ \ _) -> (abe, , R) δ(abe, _) -> (abf, , L) -δ(abf, Γ \ X) -> (abf, , L) -δ(abf, X) -> (aa, 1, L) +δ(abf, {0,1}) -> (abf, , L) +δ(abf, X) -> (ba, 0, L) -δ(abb, 1*) -> (abd, 1, R) -δ(abg, Γ \ _) -> (abg, , R) -δ(abg, _) -> (abh, , L) -δ(abh, Γ \ X) -> (abh, , L) -δ(abh, X) -> (ba, 0, L) +δ(abb, $) -> (abc, , R) + +δ(abb, {0,1}) -> (abb, , L) states b*: add the last digit of both numbers while carrying a one - read left from end of tape, after reading $, until reading: - 0: replace with 0*, goto state (baa) - 1: replace with 1*, goto state (bba) - - $: do not replace, read right until _, goto state (ca) + - $: do not replace, read right until _, goto state (za) -δ(ba, Γ \ $) -> (ba, , L) +δ(ba, {X,0,1}) -> (ba, , L) δ(ba, $) -> (bb, , L) +δ(bb, {0*,1*}) -> (bb, , L) δ(bb, 0) -> (baa, 0*, L) - δ(bb, 1) -> (bba, 1*, L) δ(bb, $) -> (bc, , R) δ(bc, Γ \ _) -> (bc, , R) -δ(bc, _) -> (ca, , L) +δ(bc, _) -> (za, , L) states ba* - read left until $, then read left until: - 0*: replace with 0, read right until _, then read left until X and replace with 1, then goto state (aa) - 1*: replace with 1, read right until _, then read left until X and replace with 0, then goto state (ba) -δ(baa, Γ \ $) -> (baa, , L) +δ(baa, {0,1}) -> (baa, , L) δ(baa, $) -> (bab, , L) δ(bab, 0*) -> (bac, 0, R) δ(bac, Γ \ _) -> (bac, , R) δ(bac, _) -> (bad, , L) -δ(bad, Γ \ X) -> (bad, , L) +δ(bad, {0,1}) -> (bad, , L) δ(bad, X) -> (aa, 1, L) -δ(bab, 1*) -> (bad, 1, R) +δ(bab, 1*) -> (bae, 1, R) δ(bae, Γ \ _) -> (bae, , R) δ(bae, _) -> (baf, , L) -δ(baf, Γ \ X) -> (baf, , L) +δ(baf, {0,1}) -> (baf, , L) δ(baf, X) -> (ba, 0, L) +δ(bab, {0,1}) -> (bab, , L) + states bb* - read left until $, then read left until: - 0*: replace with 0, read right until _, then read left until X and replace with 0, goto state (ba) - 1*: replace with 1, read right until _, then read left until X and replace with 1, goto state (ba) -δ(bba, Γ \ $) -> (bba, , L) +δ(bba, {0,1}) -> (bba, , L) δ(bba, $) -> (bbb, , L) δ(bbb, 0*) -> (bbc, 0, R) δ(bbc, Γ \ _) -> (bbc, , R) δ(bbc, _) -> (bbd, , L) -δ(bbd, Γ \ X) -> (bbd, , L) +δ(bbd, {0,1}) -> (bbd, , L) δ(bbd, X) -> (ba, 0, L) -δ(bbb, 1*) -> (bbd, 1, R) +δ(bbb, 1*) -> (bbe, 1, R) δ(bbe, Γ \ _) -> (bbe, , R) δ(bbe, _) -> (bbf, , L) -δ(bbf, Γ \ X) -> (bbf, , L) +δ(bbf, {0,1}) -> (bbf, , L) δ(bbf, X) -> (ba, 1, L) +δ(bbb, $) -> (bbc, , R) + +δ(bbb, {0,1}) -> (bbb, , L) states c*: scooting over the computed number to make space for a carried digit - read left until $, then: - read right, noting the current number and writing the previous number - then go to state (sa) -δ(ca, Γ \ $) -> (ca, , L) -δ(ca, $) -> (cb, , L) +δ(za, {0,1}) -> (za, , L) +δ(za, $) -> (zb, , R) + +δ(zb, 0) -> (zc, 1, R) +δ(zb, 1) -> (zb, 1, R) +δ(zb, _) -> (zd, 1, R) -δ(cb, Γ \ {0,1,_}) -> (cb, , R) -δ(cb, 0) -> (cc, 1, R) -δ(cb, 1) -> (cb, 1, R) -δ(cb, _) -> (sa, 1, R) +δ(zc, 0) -> (zc, 0, R) +δ(zc, 1) -> (zb, 0, R) +δ(zc, _) -> (zd, 0, R) -δ(cc, Γ \ {0,1,_}) -> (cc, , R) -δ(cc, 0) -> (cc, 0, R) -δ(cc, 1) -> (cb, 0, R) -δ(cc, _) -> (sa, 0, R) +δ(zd, _) -> (sa, $, R) |