“Towards a characterization of regular languages generated by finite splicing systems: where are we?” Ravello, 19-21 Settembre 2003 Paola Bonizzoni, Giancarlo Mauri Dipartimento di Informatica Sistemistica e Comunicazioni, Univ. of Milano - Bicocca, ITALY Clelia De Felice, Rosalba Zizza Dipartimento di Informatica e Applicazioni, Univ. of Salerno, ITALY
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Paola Bonizzoni, Giancarlo Mauri Dipartimento di Informatica Sistemistica e Comunicazioni,
“Towards a characterization of regular languages generated by finite splicing systems: where are we?” Ravello, 19-21 Settembre 2003. Paola Bonizzoni, Giancarlo Mauri Dipartimento di Informatica Sistemistica e Comunicazioni, Univ. of Milano - Bicocca, ITALY. Clelia De Felice, Rosalba Zizza - PowerPoint PPT Presentation
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“Towards a characterization of regular languages generated by finite splicing
systems: where are we?”
Ravello, 19-21 Settembre 2003
Paola Bonizzoni, Giancarlo Mauri
Dipartimento di Informatica Sistemistica e Comunicazioni,
Univ. of Milano - Bicocca, ITALY
Clelia De Felice, Rosalba Zizza
Dipartimento di Informatica e Applicazioni,
Univ. of Salerno, ITALY
COFINauditorium
COFINauditorium working on
splicing themes
after this talk
: (x u1u2 y, wu3u4 z)r = u1 | u2 $ u3 | u4 rule
(x u1 u4 z , wu3 u2 y)
Paun’s linear splicing operation (1996)
cut
paste
Pattern recognition
x y w z
sites
u1 u2 u3 u4
xw
zy
u1
u2 u3
u4
x u1 zu4 w u3 u2 y
Example
mesto, passo s| s $ s | t
me s s o, pa s t ou2u1 u4u3
L(SPA) = I (I) 2(I) ... = n0 n(I) splicing language
H(F1, F2) = {L=L(SPA) | SPA = (A,I,R), IF1, R F2, F1, F2 families in the Chomsky hierarchy}
Paun’s linear splicing system (1996) SPA = (A, I, R)
A=finite alphabet; I A* initial language; RA*|A*$A*|A* set of rules;
I \ R FIN REG LIN CF CS RE
FIN FIN,REG FIN,RE FIN,RE FIN,RE FIN,RE FIN,RE
REG REG REG,RE REG,RE REG,RE REG,RE REG,RE
LIN LIN,CF LIN,RE LIN,RE LIN,RE LIN,RE LIN,RE
CF CF CF,RE CF,RE CF,RE CF,RE CF,RE
CS CS,RE CS,RE CS,RE CS,RE CS,RE CS,RE
RE RE RE RE RE RE RE
{ L | L=L(SPA), I, R finite sets } Regular
{ L | L=L(SPA), I regular, R finite } = Regular
(aa)* L(SPA) (proper subclass)
[Head, Paun, Pixton,Handbook of Formal Languages, 1996]H(F1, F2)
Finite linear splicing system: SPA = ( A, I, R) with A, I, R finite sets
In the following…In the following…
Characterize regular languages generated by finite linear Paun splicing
systemsProblem 1
Problem 2Given L regular,
can we decide whether L H(FIN,FIN) ?
Computational power of splicing languages and regular languages: a short survey…
Head 1987 (Bull. Math. Biol.): SLT=languages generated by Null Context splicing systems
(triples (1,x,1))
Gatterdam 1992 (SIAM J. of Comp.): specific finite Head’s splicing systems
Culik, Harju 1992 (Discr. App. Math.): (Head’s) splicing and domino languages
Kim 1997 (SIAM J. of Comp.): from the finite state automaton recognizing I to the f.s.a.
recognizing L(SH)
Kim 1997 (Cocoon97): given LREG, a finite set of triples X, we can decide whether IL s.t.
L= L(SH)
Pixton 1996 (Theor. Comp. Sci.): if F is a full AFL, then H(FA,FIN) FA