Eventually, the whole process may terminate,
which we achieve in a Turing machine by putting
it into a halt state. A Turing machine is said
to halt whenever it reaches a configuration for
which δ is not defined; this is possible because
δ is a partial function. In fact, we will assume
that no transitions are defined for any final
state, so the Turing machine will halt whenever
it enters a final state. page 1990:234 Linz
Linz, Peter 1990. An Introduction to Formal Languages and Automata. Lexington/Toronto: D. C. Heath and Company. (317-320)
On 2025-09-10 11:31:00 +0000, olcott said:
Eventually, the whole process may terminate,
which we achieve in a Turing machine by putting
it into a halt state. A Turing machine is said
to halt whenever it reaches a configuration for
which δ is not defined; this is possible because
δ is a partial function. In fact, we will assume
that no transitions are defined for any final
state, so the Turing machine will halt whenever
it enters a final state. page 1990:234 Linz
Linz, Peter 1990. An Introduction to Formal Languages and Automata.
Lexington/Toronto: D. C. Heath and Company. (317-320)
I stated in news:109ojic$ract$1@dont-email.me that "About Turing
machines it means a configuration for which the rules don't specfy
any action." Above Linz says the same.
On 8/2/2024 7:19 PM, Mike Terry wrote:--
Definition: A TM P given input I is said to "halt" iff ?????
or whatever...
I think this is a rather hopeless venture without
formally defining the representation of a TM. For
example: In some formulations, there are specific
states defined as "halting states" and the machine
only halts if either the start state is a halt state or
there is a transition to a halt state within the execution
trace; In another formulation, machines halt if there
is a transition to an undefined state. Note a few things:
1) the if's above are really iff's, 2) these and many
other definitions all have equivalent computing prowess,
3) Some formulations define results by what is left on
the tape (or other storage device) while others add the
actual halting state to determine the results.
In a conversation about such topics, gentlemen of good
faith and reasonable knowledge can simple ignore these
differences and not go off the rails.
On 9/11/2025 4:01 AM, Mikko wrote:
On 2025-09-10 11:31:00 +0000, olcott said:
Eventually, the whole process may terminate,
which we achieve in a Turing machine by putting
it into a halt state. A Turing machine is said
to halt whenever it reaches a configuration for
which δ is not defined; this is possible because
δ is a partial function. In fact, we will assume
that no transitions are defined for any final
state, so the Turing machine will halt whenever
it enters a final state. page 1990:234 Linz
Linz, Peter 1990. An Introduction to Formal Languages and Automata.
Lexington/Toronto: D. C. Heath and Company. (317-320)
I stated in news:109ojic$ract$1@dont-email.me that "About Turing
machines it means a configuration for which the rules don't specfy
any action." Above Linz says the same.
And also says the Turing machine will halt whenever
it enters a final state.
On 2025-09-11 15:48:42 +0000, olcott said:
On 9/11/2025 4:01 AM, Mikko wrote:
On 2025-09-10 11:31:00 +0000, olcott said:
Eventually, the whole process may terminate,
which we achieve in a Turing machine by putting
it into a halt state. A Turing machine is said
to halt whenever it reaches a configuration for
which δ is not defined; this is possible because
δ is a partial function. In fact, we will assume
that no transitions are defined for any final
state, so the Turing machine will halt whenever
it enters a final state. page 1990:234 Linz
Linz, Peter 1990. An Introduction to Formal Languages and Automata.
Lexington/Toronto: D. C. Heath and Company. (317-320)
I stated in news:109ojic$ract$1@dont-email.me that "About Turing
machines it means a configuration for which the rules don't specfy
any action." Above Linz says the same.
And also says the Turing machine will halt whenever
it enters a final state.
That is obvious when "final state" is defined as a state where
the Turing machine halts.
But Linz does not say that as a part of the definition of halting.
After the definition he says he assumes that in his Turing machine
every state has rules for either every or no tape symbol. Other
author permit and in some cases requite that a Turing machine has
a state that has a rule for some but not all possible tape symbols,
and call such states as "reject" states.
But in any case, as Linz says, "said to halt whenever it reaches a configuration for which δ is not defined", where δ is the partial
function that determines the next configuration of the Turing
machine. That agrees with the usual meaning of "halt".
On 8/2/2024 7:19 PM, Mike Terry wrote:--
Definition: A TM P given input I is said to "halt" iff ?????
or whatever...
I think this is a rather hopeless venture without
formally defining the representation of a TM. For
example: In some formulations, there are specific
states defined as "halting states" and the machine
only halts if either the start state is a halt state or
there is a transition to a halt state within the execution
trace; In another formulation, machines halt if there
is a transition to an undefined state. Note a few things:
1) the if's above are really iff's, 2) these and many
other definitions all have equivalent computing prowess,
3) Some formulations define results by what is left on
the tape (or other storage device) while others add the
actual halting state to determine the results.
In a conversation about such topics, gentlemen of good
faith and reasonable knowledge can simple ignore these
differences and not go off the rails.
On 9/12/2025 1:34 AM, Mikko wrote:
On 2025-09-11 15:48:42 +0000, olcott said:
On 9/11/2025 4:01 AM, Mikko wrote:
On 2025-09-10 11:31:00 +0000, olcott said:
Eventually, the whole process may terminate,
which we achieve in a Turing machine by putting
it into a halt state. A Turing machine is said
to halt whenever it reaches a configuration for
which δ is not defined; this is possible because
δ is a partial function. In fact, we will assume
that no transitions are defined for any final
state, so the Turing machine will halt whenever
it enters a final state. page 1990:234 Linz
Linz, Peter 1990. An Introduction to Formal Languages and Automata. >>>>> Lexington/Toronto: D. C. Heath and Company. (317-320)
I stated in news:109ojic$ract$1@dont-email.me that "About Turing
machines it means a configuration for which the rules don't specfy
any action." Above Linz says the same.
And also says the Turing machine will halt whenever
it enters a final state.
That is obvious when "final state" is defined as a state where
the Turing machine halts.
But Linz does not say that as a part of the definition of halting.
After the definition he says he assumes that in his Turing machine
every state has rules for either every or no tape symbol. Other
author permit and in some cases requite that a Turing machine has
a state that has a rule for some but not all possible tape symbols,
and call such states as "reject" states.
But in any case, as Linz says, "said to halt whenever it reaches a
configuration for which δ is not defined", where δ is the partial
function that determines the next configuration of the Turing
machine. That agrees with the usual meaning of "halt".
This is our own Jeff, make sure you read his
last paragraph
On 8/2/2024 11:32 PM, Jeff Barnett wrote:
On 8/2/2024 7:19 PM, Mike Terry wrote:
Definition: A TM P given input I is said to "halt" iff ?????
or whatever...
I think this is a rather hopeless venture without
formally defining the representation of a TM. For
example: In some formulations, there are specific
states defined as "halting states" and the machine
only halts if either the start state is a halt state or
there is a transition to a halt state within the execution
trace; In another formulation, machines halt if there
is a transition to an undefined state. Note a few things:
1) the if's above are really iff's, 2) these and many
other definitions all have equivalent computing prowess,
3) Some formulations define results by what is left on
the tape (or other storage device) while others add the
actual halting state to determine the results.
In a conversation about such topics, gentlemen of good
faith and reasonable knowledge can simple ignore these
differences and not go off the rails.
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