scholarly journals Hereditary History Preserving Simulation is Undecidable

1999 ◽  
Vol 6 (1) ◽  
Author(s):  
Marcin Jurdzinski ◽  
Mogens Nielsen
Keyword(s):  
Simulation Game ◽  
Turing Machines ◽  
Transition Systems ◽  
Halting Problem ◽  
Intermediate Problem

We show undecidability of hereditary history preserving simulation<br />for finite asynchronous transition systems by a reduction from the halting<br />problem of deterministic Turing machines. To make the proof more<br />transparent we introduce an intermediate problem of deciding the winner<br />in domino snake games. First we reduce the halting problem of deterministic<br />Turing machines to domino snake games. Then we show how to<br />model a domino snake game by a hereditary history simulation game on<br />a pair of finite asynchronous transition systems.

scholarly journals Hereditary History Preserving Bisimilarity is Undecidable

1999 ◽  
Vol 6 (19) ◽  
Author(s):  
Marcin Jurdzinski ◽  
Mogens Nielsen
Keyword(s):  
Petri Nets ◽  
Transition Systems ◽  
Halting Problem ◽  
Proper Subclass ◽  
Intermediate Problem ◽  
Tiling Systems ◽  
Counter Machines ◽  
Undecidability Result

We show undecidability of hereditary history preserving bisimilarity<br />for finite asynchronous transition systems by a reduction from the halting<br />problem of deterministic 2-counter machines. To make the proof more<br />transparent we introduce an intermediate problem of checking domino<br />bisimilarity for origin constrained tiling systems. First we reduce the<br />halting problem of deterministic 2-counter machines to origin constrained<br />domino bisimilarity. Then we show how to model domino bisimulations as<br />hereditary history preserving bisimulations for finite asynchronous transitions<br />systems. We also argue that the undecidability result holds for<br />finite 1-safe Petri nets, which can be seen as a proper subclass of finite<br />asynchronous transition systems.

The unsolvability of the uniform halting problem for two state Turing machines

1969 ◽  
Vol 34 (2) ◽  
pp. 161-165 ◽  
Author(s):  
Gabor T. Herman
Keyword(s):  
Finite Number ◽  
Turing Machine ◽  
Decision Procedure ◽  
Turing Machines ◽  
Halting Problem

The uniform halting problem (UH) can be stated as follows:Give a decision procedure which for any given Turing machine (TM) will decide whether or not it has an immortal instantaneous description (ID).An ID is called immortal if it has no terminal successor. As it is generally the case in the literature (see e.g. Minsky [4, p. 118]) we assume that in an ID the tape must be blank except for some finite number of squares. If we remove this restriction the UH becomes the immortality problem (IP).

High and low Kleene degrees of coanalytic sets

1983 ◽  
Vol 48 (2) ◽  
pp. 356-368 ◽  
Author(s):  
Stephen G. Simpson ◽  
Galen Weitkamp
Keyword(s):  
Characteristic Function ◽  
Cross Section ◽  
Finite Time ◽  
Infinite Sequence ◽  
Turing Machines ◽  
Jump Operator ◽  
Halting Problem ◽  
Computing Machine ◽  
Definition Of ◽  
Countably Infinite

We say that a set A of reals is recursive in a real y together with a set B of reals if one can imagine a computing machine with an ability to perform a countably infinite sequence of program steps in finite time and with oracles for B and y so that decides membership in A for any real x input to by way of an oracle for x. We write A ≤ yB. A precise definition of this notion of recursion was first considered in Kleene [9]. In the notation of that paper, A ≤yB if there is an integer e so that χA(x) = {e}(x y, χB, 2E). Here χA is the characteristic function of A. Thus Kleene would say that A is recursive in (y, B, 2E), where 2E is the existential integer quantifier.Gandy [5] observes that the halting problem for infinitary machines such as , as in the case of Turing machines, gives rise to a jump operator for higher type recursion. Thus given a set B of reals, the superjump B′ of B is defined to be the set of all triples 〈e, x, y〉 such that the eth machine with oracles for y and B eventually halts when given input x. A set A is said to be semirecursive in y together with B if for some integer e, A is the cross section {x: 〈e, x, y 〉 ∈ B′}. In Kleene [9] it is demonstrated that a set A is semirecursive in y alone if and only if it is

scholarly journals Turing machines, transition systems, and interaction

2004 ◽  
Vol 194 (2) ◽  
pp. 101-128 ◽  
Author(s):  
Dina Q. Goldin ◽  
Scott A. Smolka ◽  
Paul C. Attie ◽  
Elaine L. Sonderegger
Keyword(s):  
Turing Machines ◽  
Transition Systems

scholarly journals Translatability Problem of Geodesics on Algorithmic Manifolds

2016 ◽  
Author(s):  
Takuya Yabu
Keyword(s):  
Turing Machine ◽  
Optimal Algorithm ◽  
Turing Machines ◽  
Halting Problem ◽  
End Point ◽  
Np Problem

In the previous paper, I define algorithmic manifolds simulating deterministic Turing machines and by determining the start point and end point of the algorithm in a P problem on the algorithmic manifold, there is the optimal algorithm as the length minimizing geodesic between the start point and the end point, and the length minimizing geodesic can be derived by determining the start point and the end point also in a NP problem.　In this paper, I show that the possibility of translating algorithms from geodesics on algorithmic manifolds is equivalent to the halting problem of Turing machine. I will also discuss the problems of translating from geodesics using existing algorithms.

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