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PCP & MPCP

PCP(Post's Correspondence Problem)
MPCP(Modified PCP)

PCP consists of two lists A=w1,....,wk and
B=x1,....,xk , of strings over some alphabets SIGMA.
This instance of PCP has a solution if there is any sequence of integers i1,i2,.....,im,with m>=1. Such that

wi1,wi2,....,wim=xi1,xi2,....,xim.
The sequence i1,....,im is a solution to this instance of PCP.

MPCP 
Lists A & B of k strings each from Sigma*.say
A=w1,w2,...,wk
and
B=x1,x2,.....,xk
does there exist a sequence of integers i1,i2,....,ir.
such that
w1 wi1 wi2 .... wir=x1 xi1 xi2 ..... xir ?

Difference between PCP and MPCP is that in the MPCP, a solution is required to start with the first string on each list.



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