What is the Name of the Problem or Technique of Determining if a Line in a Program Will Execute












3












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If I were to pose the question: "Given a program $P$ containing statement $X$, will $X$ be executed (given enough runs with all possible inputs)?"



This strikes me of being a relative of the Halting Problem, but I just don't know the taxonomy here.



What is the name of this problem, or does it not have a name because it is solved/uninteresting?






computability rice-theorem







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    3












    $begingroup$


    If I were to pose the question: "Given a program $P$ containing statement $X$, will $X$ be executed (given enough runs with all possible inputs)?"



    This strikes me of being a relative of the Halting Problem, but I just don't know the taxonomy here.



    What is the name of this problem, or does it not have a name because it is solved/uninteresting?






    computability rice-theorem







    share|cite|improve this question









    New contributor




    Keenan Diggs is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
    Check out our Code of Conduct.







    $endgroup$















      3












      3








      3





      $begingroup$


      If I were to pose the question: "Given a program $P$ containing statement $X$, will $X$ be executed (given enough runs with all possible inputs)?"



      This strikes me of being a relative of the Halting Problem, but I just don't know the taxonomy here.



      What is the name of this problem, or does it not have a name because it is solved/uninteresting?






      computability rice-theorem







      share|cite|improve this question









      New contributor




      Keenan Diggs is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.







      $endgroup$




      If I were to pose the question: "Given a program $P$ containing statement $X$, will $X$ be executed (given enough runs with all possible inputs)?"



      This strikes me of being a relative of the Halting Problem, but I just don't know the taxonomy here.



      What is the name of this problem, or does it not have a name because it is solved/uninteresting?






      computability rice-theorem




      computability rice-theorem






      share|cite|improve this question









      New contributor




      Keenan Diggs is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.











      share|cite|improve this question









      New contributor




      Keenan Diggs is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.









      share|cite|improve this question




      share|cite|improve this question








      edited 3 hours ago









      PyRulez

      316114




      316114






      New contributor




      Keenan Diggs is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.









      asked 7 hours ago









      Keenan DiggsKeenan Diggs

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      Keenan Diggs is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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      New contributor





      Keenan Diggs is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.






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      Check out our Code of Conduct.






















          2 Answers
          2






          active

          oldest

          votes


















          4












          $begingroup$

          EDIT: This answer is more detailed than mine.



          This is an example of a question covered by Rice's theorem. For example, the question of if a program outputs "Hello World" or not is covered by that theorem.



          It also covers quantification over inputs (e.g. does program $P$ do $X$ on all input, does program $P$ do $X$ on some inputs, does program $P$ do $X$ on even inputs, etc...).



          In particular, it states that in general, the problem is only semidecidable, just like the Halting problem.



          EDIT: The theorem is only about what a program does, not its internals. So the question of "does a program ever get to line 7?" technically is not covered by the theorem. To get around this, just imagine that your interpreter/compiler prints out the line number it is currently on. Now the question is "does the program ever say it is on line 7?", which is a question about what it does, and therefore covered by Rice's theorem. You do not need to actually make the modification; just proving the possibility is enough.






          share|cite|improve this answer











          $endgroup$













          • $begingroup$
            Thank you for answering my question. I will continue my research toward Rice's Theorem.
            $endgroup$
            – Keenan Diggs
            7 hours ago






          • 1




            $begingroup$
            @KeenanDiggs if you have any other questions, let me know.
            $endgroup$
            – PyRulez
            7 hours ago










          • $begingroup$
            @KeenanDiggs Also, I added a caveat to the answer.
            $endgroup$
            – PyRulez
            4 hours ago



















          3












          $begingroup$

          This is called the reachability problem -- is it possible for a given system to enter a given state?



          Techniques that attempt to answer this problem fall under reachability analysis, which is one of the main goals of (finite / symbolic) model checking.




          As the other answer suggests, this is one of the many instances covered by Rice's theorem. Answering questions about the runtime behavior of programs from only their source code is almost always undecidable. Nonetheless, there are many attempts to solve these problems that can be fairly effective in "real world" code (e.g., Microsoft's 2002 project SLAM), because human programmers tend to try to make their code easy to understand (for other humans; we hope incidentally also for mechanical analysis)






          share|cite|improve this answer









          $endgroup$













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            2 Answers
            2






            active

            oldest

            votes








            2 Answers
            2






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes









            4












            $begingroup$

            EDIT: This answer is more detailed than mine.



            This is an example of a question covered by Rice's theorem. For example, the question of if a program outputs "Hello World" or not is covered by that theorem.



            It also covers quantification over inputs (e.g. does program $P$ do $X$ on all input, does program $P$ do $X$ on some inputs, does program $P$ do $X$ on even inputs, etc...).



            In particular, it states that in general, the problem is only semidecidable, just like the Halting problem.



            EDIT: The theorem is only about what a program does, not its internals. So the question of "does a program ever get to line 7?" technically is not covered by the theorem. To get around this, just imagine that your interpreter/compiler prints out the line number it is currently on. Now the question is "does the program ever say it is on line 7?", which is a question about what it does, and therefore covered by Rice's theorem. You do not need to actually make the modification; just proving the possibility is enough.






            share|cite|improve this answer











            $endgroup$













            • $begingroup$
              Thank you for answering my question. I will continue my research toward Rice's Theorem.
              $endgroup$
              – Keenan Diggs
              7 hours ago






            • 1




              $begingroup$
              @KeenanDiggs if you have any other questions, let me know.
              $endgroup$
              – PyRulez
              7 hours ago










            • $begingroup$
              @KeenanDiggs Also, I added a caveat to the answer.
              $endgroup$
              – PyRulez
              4 hours ago
















            4












            $begingroup$

            EDIT: This answer is more detailed than mine.



            This is an example of a question covered by Rice's theorem. For example, the question of if a program outputs "Hello World" or not is covered by that theorem.



            It also covers quantification over inputs (e.g. does program $P$ do $X$ on all input, does program $P$ do $X$ on some inputs, does program $P$ do $X$ on even inputs, etc...).



            In particular, it states that in general, the problem is only semidecidable, just like the Halting problem.



            EDIT: The theorem is only about what a program does, not its internals. So the question of "does a program ever get to line 7?" technically is not covered by the theorem. To get around this, just imagine that your interpreter/compiler prints out the line number it is currently on. Now the question is "does the program ever say it is on line 7?", which is a question about what it does, and therefore covered by Rice's theorem. You do not need to actually make the modification; just proving the possibility is enough.






            share|cite|improve this answer











            $endgroup$













            • $begingroup$
              Thank you for answering my question. I will continue my research toward Rice's Theorem.
              $endgroup$
              – Keenan Diggs
              7 hours ago






            • 1




              $begingroup$
              @KeenanDiggs if you have any other questions, let me know.
              $endgroup$
              – PyRulez
              7 hours ago










            • $begingroup$
              @KeenanDiggs Also, I added a caveat to the answer.
              $endgroup$
              – PyRulez
              4 hours ago














            4












            4








            4





            $begingroup$

            EDIT: This answer is more detailed than mine.



            This is an example of a question covered by Rice's theorem. For example, the question of if a program outputs "Hello World" or not is covered by that theorem.



            It also covers quantification over inputs (e.g. does program $P$ do $X$ on all input, does program $P$ do $X$ on some inputs, does program $P$ do $X$ on even inputs, etc...).



            In particular, it states that in general, the problem is only semidecidable, just like the Halting problem.



            EDIT: The theorem is only about what a program does, not its internals. So the question of "does a program ever get to line 7?" technically is not covered by the theorem. To get around this, just imagine that your interpreter/compiler prints out the line number it is currently on. Now the question is "does the program ever say it is on line 7?", which is a question about what it does, and therefore covered by Rice's theorem. You do not need to actually make the modification; just proving the possibility is enough.






            share|cite|improve this answer











            $endgroup$



            EDIT: This answer is more detailed than mine.



            This is an example of a question covered by Rice's theorem. For example, the question of if a program outputs "Hello World" or not is covered by that theorem.



            It also covers quantification over inputs (e.g. does program $P$ do $X$ on all input, does program $P$ do $X$ on some inputs, does program $P$ do $X$ on even inputs, etc...).



            In particular, it states that in general, the problem is only semidecidable, just like the Halting problem.



            EDIT: The theorem is only about what a program does, not its internals. So the question of "does a program ever get to line 7?" technically is not covered by the theorem. To get around this, just imagine that your interpreter/compiler prints out the line number it is currently on. Now the question is "does the program ever say it is on line 7?", which is a question about what it does, and therefore covered by Rice's theorem. You do not need to actually make the modification; just proving the possibility is enough.







            share|cite|improve this answer














            share|cite|improve this answer



            share|cite|improve this answer








            edited 2 hours ago

























            answered 7 hours ago









            PyRulezPyRulez

            316114




            316114












            • $begingroup$
              Thank you for answering my question. I will continue my research toward Rice's Theorem.
              $endgroup$
              – Keenan Diggs
              7 hours ago






            • 1




              $begingroup$
              @KeenanDiggs if you have any other questions, let me know.
              $endgroup$
              – PyRulez
              7 hours ago










            • $begingroup$
              @KeenanDiggs Also, I added a caveat to the answer.
              $endgroup$
              – PyRulez
              4 hours ago


















            • $begingroup$
              Thank you for answering my question. I will continue my research toward Rice's Theorem.
              $endgroup$
              – Keenan Diggs
              7 hours ago






            • 1




              $begingroup$
              @KeenanDiggs if you have any other questions, let me know.
              $endgroup$
              – PyRulez
              7 hours ago










            • $begingroup$
              @KeenanDiggs Also, I added a caveat to the answer.
              $endgroup$
              – PyRulez
              4 hours ago
















            $begingroup$
            Thank you for answering my question. I will continue my research toward Rice's Theorem.
            $endgroup$
            – Keenan Diggs
            7 hours ago




            $begingroup$
            Thank you for answering my question. I will continue my research toward Rice's Theorem.
            $endgroup$
            – Keenan Diggs
            7 hours ago




            1




            1




            $begingroup$
            @KeenanDiggs if you have any other questions, let me know.
            $endgroup$
            – PyRulez
            7 hours ago




            $begingroup$
            @KeenanDiggs if you have any other questions, let me know.
            $endgroup$
            – PyRulez
            7 hours ago












            $begingroup$
            @KeenanDiggs Also, I added a caveat to the answer.
            $endgroup$
            – PyRulez
            4 hours ago




            $begingroup$
            @KeenanDiggs Also, I added a caveat to the answer.
            $endgroup$
            – PyRulez
            4 hours ago











            3












            $begingroup$

            This is called the reachability problem -- is it possible for a given system to enter a given state?



            Techniques that attempt to answer this problem fall under reachability analysis, which is one of the main goals of (finite / symbolic) model checking.




            As the other answer suggests, this is one of the many instances covered by Rice's theorem. Answering questions about the runtime behavior of programs from only their source code is almost always undecidable. Nonetheless, there are many attempts to solve these problems that can be fairly effective in "real world" code (e.g., Microsoft's 2002 project SLAM), because human programmers tend to try to make their code easy to understand (for other humans; we hope incidentally also for mechanical analysis)






            share|cite|improve this answer









            $endgroup$


















              3












              $begingroup$

              This is called the reachability problem -- is it possible for a given system to enter a given state?



              Techniques that attempt to answer this problem fall under reachability analysis, which is one of the main goals of (finite / symbolic) model checking.




              As the other answer suggests, this is one of the many instances covered by Rice's theorem. Answering questions about the runtime behavior of programs from only their source code is almost always undecidable. Nonetheless, there are many attempts to solve these problems that can be fairly effective in "real world" code (e.g., Microsoft's 2002 project SLAM), because human programmers tend to try to make their code easy to understand (for other humans; we hope incidentally also for mechanical analysis)






              share|cite|improve this answer









              $endgroup$
















                3












                3








                3





                $begingroup$

                This is called the reachability problem -- is it possible for a given system to enter a given state?



                Techniques that attempt to answer this problem fall under reachability analysis, which is one of the main goals of (finite / symbolic) model checking.




                As the other answer suggests, this is one of the many instances covered by Rice's theorem. Answering questions about the runtime behavior of programs from only their source code is almost always undecidable. Nonetheless, there are many attempts to solve these problems that can be fairly effective in "real world" code (e.g., Microsoft's 2002 project SLAM), because human programmers tend to try to make their code easy to understand (for other humans; we hope incidentally also for mechanical analysis)






                share|cite|improve this answer









                $endgroup$



                This is called the reachability problem -- is it possible for a given system to enter a given state?



                Techniques that attempt to answer this problem fall under reachability analysis, which is one of the main goals of (finite / symbolic) model checking.




                As the other answer suggests, this is one of the many instances covered by Rice's theorem. Answering questions about the runtime behavior of programs from only their source code is almost always undecidable. Nonetheless, there are many attempts to solve these problems that can be fairly effective in "real world" code (e.g., Microsoft's 2002 project SLAM), because human programmers tend to try to make their code easy to understand (for other humans; we hope incidentally also for mechanical analysis)







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered 2 hours ago









                Curtis FCurtis F

                314110




                314110






















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