Introduction to Computational Theory. Chapter 6. Front pad. Rear pad. Front, Rear, Both. Rear, Both, Neither. Front. closed. open. Neither. Automatic Door/FA. Nondeterministic. When the ultimate path through a machine is not determined by input alone the machine is nondeterministic .
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Frontpad
Rearpad
Front,Rear,Both
Rear,Both,Neither
Front
closed
open
Neither
Automatic Door/FACohen, Chapter 6
When the ultimate path through a machine is not determined by input alone the machine is nondeterministic.
Cohen, Chapter 6
Cohen, Chapter 6
Cohen, Chapter 6
Cohen, Chapter 6
Cohen, Chapter 6
+

+
baa
baa
All else
a,b
All else
a,b
Transition GraphsAbandon the requirement that the edges eat just one letter at a time.
Cohen, Chapter 6
When an input string that has not been completely read reaches a state (final or otherwise) that it cannot leave because there is no outgoing edge that it may follow, we say that the input (or the machine) crashes at that state.
Cohen, Chapter 6
+
a,b
aa, bb
a,b
Rejected Inputbaa
Cohen, Chapter 6
A string is accepted by a TG if there is some way it could be processed as to arrive at a final state.
There may also be ways in which this string does not get to a final state, but we ignore all failures.
Cohen, Chapter 6
A collection of three things:
1. A finite set of states, at least one of which is designated as the start state () and some (maybe none) of which are designated as final states (+)
2. An alphabet of possible input letters from which input strings are formed.
3. A finite set of transitions (edge labels) that show how to go from some states to some others, based on reading specified substrings of input letters (possibly even the null string )
Cohen, Chapter 6
3
Free Ride
Successful PathA successful path through a transition graph is a series of edges forming a path beginning at some start state (there may be several) and ending at a final state.
abbab…
abbaa…
abb
a
abbababba
1
4+
aa
b
A Lambda transition occurs when you get a free transition that was not initiated by user or system action/interaction. Move on a whim (w/o consuming input).Slide modified by Seals
Cohen, Chapter 6
Cohen, Chapter 6
A collection of three things:
1. A finite set of states, at least one of which is designated as the start state () and some (maybe none) of which are designated as final states (+)
2. An alphabet of possible input letters from which input strings are formed.
3. Directed edges connecting some pairs of states, each labeled with a regular expression.
Cohen, Chapter 6