My Math Forum Partial functions modelled by Labelled Transition Systems

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 October 3rd, 2014, 11:40 PM #1 Newbie   Joined: Oct 2014 From: italy Posts: 1 Thanks: 0 Partial functions modelled by Labelled Transition Systems Hi there! I'm new in this forum and I'm looking for an help to solve an exercise from my Formal Languages' Course at the university... I'll write down the assignment and then I'll ask some questions... Let Q be the set of partial functions from integers to integers. In symbols, Q={ f | f:Z->Z U{undefined} }, where f(x)= undefined models the fact that the function f is undefined on x. Let S = (Q, ZxZ, ->, {f0}), where f0(x)=undefined for all x belonging to Z, and the transition relation is defined by the following rule: IF ( f(x)=undefined ) THEN ( f(x,v) --> f{v/x} ) WHERE : f {v/x}(y)=v if x=y, OR f{v/x}(y)=f(y) otherwise. Describe informally the set of traces of S. Does S have infinite traces? What is the cardinality of Q? Is it true that any machine for S would require an infinite amount of space to represent the state of S? I know that what I've written is very clumbsy... Sorry for that... The first thing I need to understand is the meaning of the {} notation, why do we use f{something}(sth) and what are we modelling? The other thing I didn't catch is whether there are transitions or not: if f0 is the initial state BUT it is always undefined (for all x in Z) then we'll never move from this state to another one... Isn't this correct? Please HELP ME... I'm stubbornly looking at this exercise from days and days without any idea... What I need is at least a small clue!!!! Byeee (and sorry for my bad english!!! ) Last edited by akil78; October 3rd, 2014 at 11:45 PM.

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