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Directory:Jon Awbrey/Papers/Differential Analytic Turing Automata (view source)

Revision as of 03:38, 18 March 2009

58 bytes added ,  03:38, 18 March 2009
descriptive headings
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The ''tape head'' (that is, the ''read unit'') will be called <math>\operatorname{H}.</math>  The ''registers'' are also called ''tape cells'' or ''tape squares''.
 
The ''tape head'' (that is, the ''read unit'') will be called <math>\operatorname{H}.</math>  The ''registers'' are also called ''tape cells'' or ''tape squares''.
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==Note 22==
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===Finite Approximations===
    
To see how each finite approximation to a given turing machine can be given a purely propositional description, one fixes the parameter <math>k\!</math> and limits the rest of the discussion to describing <math>\operatorname{Stilt}(k),</math> which is not really a full-fledged TM anymore but just a finite automaton in disguise.
 
To see how each finite approximation to a given turing machine can be given a purely propositional description, one fixes the parameter <math>k\!</math> and limits the rest of the discussion to describing <math>\operatorname{Stilt}(k),</math> which is not really a full-fledged TM anymore but just a finite automaton in disguise.
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|}
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==Initial Conditions==
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===Initial Conditions===
    
Given but a single free square on the tape, there are just two different sets of initial conditions for <math>\operatorname{Stunt}(2),</math> the finite approximation to the parity turing machine that we are presently considering.
 
Given but a single free square on the tape, there are just two different sets of initial conditions for <math>\operatorname{Stunt}(2),</math> the finite approximation to the parity turing machine that we are presently considering.
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===Initial Conditions for Tape Input "0"===
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====Initial Conditions for Tape Input "0"====
    
The following conjunction of 5 basic propositions describes the initial conditions when <math>\operatorname{Stunt}(2)</math> is started with an input of "0" in its free square:
 
The following conjunction of 5 basic propositions describes the initial conditions when <math>\operatorname{Stunt}(2)</math> is started with an input of "0" in its free square:
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===Initial Conditions for Tape Input "1"===
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====Initial Conditions for Tape Input "1"====
    
The following conjunction of 5 basic propositions describes the initial conditions when <math>\operatorname{Stunt}(2)</math> is started with an input of "1" in its free square:
 
The following conjunction of 5 basic propositions describes the initial conditions when <math>\operatorname{Stunt}(2)</math> is started with an input of "1" in its free square:
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==Propositional Program==
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===Propositional Program===
    
A complete description of <math>\operatorname{Stunt}(2)</math> in propositional form is obtained by conjoining one of the above choices for initial conditions with all of the following sets of propositions, that serve in effect as a simple type of ''declarative program'', telling us all that we need to know about the anatomy and behavior of the truncated TM in question.
 
A complete description of <math>\operatorname{Stunt}(2)</math> in propositional form is obtained by conjoining one of the above choices for initial conditions with all of the following sets of propositions, that serve in effect as a simple type of ''declarative program'', telling us all that we need to know about the anatomy and behavior of the truncated TM in question.
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===Mediate Conditions===
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====Mediate Conditions====
    
{| align="center" cellpadding="8" width="90%"
 
{| align="center" cellpadding="8" width="90%"
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|}
 
|}
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===Terminal Conditions===
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====Terminal Conditions====
    
{| align="center" cellpadding="8" width="90%"
 
{| align="center" cellpadding="8" width="90%"
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|}
 
|}
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===State Partition===
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====State Partition====
    
{| align="center" cellpadding="8" width="90%"
 
{| align="center" cellpadding="8" width="90%"
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|}
 
|}
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===Register Partition===
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====Register Partition====
    
{| align="center" cellpadding="8" width="90%"
 
{| align="center" cellpadding="8" width="90%"
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|}
 
|}
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===Symbol Partition===
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====Symbol Partition====
    
{| align="center" cellpadding="8" width="90%"
 
{| align="center" cellpadding="8" width="90%"
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|}
 
|}
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===Interaction Conditions===
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====Interaction Conditions====
    
{| align="center" cellpadding="8" width="90%"
 
{| align="center" cellpadding="8" width="90%"
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|}
 
|}
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===Transition Relations===
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====Transition Relations====
    
{| align="center" cellpadding="8" width="90%"
 
{| align="center" cellpadding="8" width="90%"
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|}
 
|}
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==Interpretation of the Propositional Program==
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===Interpretation of the Propositional Program===
    
Let us now run through the propositional specification of <math>\operatorname{Stunt}(2),</math> our truncated TM, and paraphrase what it says in ordinary language.
 
Let us now run through the propositional specification of <math>\operatorname{Stunt}(2),</math> our truncated TM, and paraphrase what it says in ordinary language.
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===Mediate Conditions===
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====Mediate Conditions====
    
{| align="center" cellpadding="8" width="90%"
 
{| align="center" cellpadding="8" width="90%"
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|}
 
|}
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===Terminal Conditions===
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====Terminal Conditions====
    
{| align="center" cellpadding="8" width="90%"
 
{| align="center" cellpadding="8" width="90%"
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|}
 
|}
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===State Partition===
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====State Partition====
    
{| align="center" cellpadding="8" width="90%"
 
{| align="center" cellpadding="8" width="90%"
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|}
 
|}
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===Register Partition===
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====Register Partition====
    
{| align="center" cellpadding="8" width="90%"
 
{| align="center" cellpadding="8" width="90%"
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|}
 
|}
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===Symbol Partition===
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====Symbol Partition====
    
{| align="center" cellpadding="8" width="90%"
 
{| align="center" cellpadding="8" width="90%"
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|}
 
|}
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===Interaction Conditions===
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====Interaction Conditions====
    
{| align="center" cellpadding="8" width="90%"
 
{| align="center" cellpadding="8" width="90%"
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The eighteen clauses of the Interaction Conditions simply impose one such constraint on symbol changes for each combination of the times <math>p_0, p_1,\!</math> registers <math>r_0, r_1, r_2,\!</math> and symbols <math>s_0, s_1, s_\#.\!</math>
 
The eighteen clauses of the Interaction Conditions simply impose one such constraint on symbol changes for each combination of the times <math>p_0, p_1,\!</math> registers <math>r_0, r_1, r_2,\!</math> and symbols <math>s_0, s_1, s_\#.\!</math>
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===Transition Relations===
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====Transition Relations====
    
{| align="center" cellpadding="8" width="90%"
 
{| align="center" cellpadding="8" width="90%"
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|}
 
|}
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==Note 32==
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===Note 32===
    
<pre>
 
<pre>
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</pre>
 
</pre>
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==Note 33==
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===Note 33===
    
<pre>
 
<pre>
Jon Awbrey
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