fertin.blogg.se - Stack the states 2 game

$(c,0,\text) \to (c,s)$ if the state is not $\langle dir\rangle$ don't move, do whatever you like with the state. TheĬomputation stops when a special halting state is reached.Ĭhoose a universal Turing machine with $S$ states ($0\leq s 0$ move, flip the state. Right (and cannot stay reading the same cell), and the state is modified. The symbol read by the head, the symbol is modified, the head moves left or At each step, according to the current state of the machine and Symbol, the head reads the leftmost symbol of the input, and the state is the Initially, aįinite word, the input, is written on the tape, other cells contain the blank They have a unique one-dimensional tape infinite in both directions, and a unique twoway The notion of TM used in the paper is the standard definition of TM used in papers on small universal Turing machines : (perhaps some results have been improved). I quickly read it some time ago, and it has a nice graph with the borderlines between the 4 types of small TMs: This is not a real answer to your question (I don't know much about the (2,3) machine debate) but I suggest you the paper " Small Turing machines and generalized busy beaver competition". Machine models (taken from Neary, Woods SOFSEM 2012), The figure shows the smallest known universal machines for a variety of Turing (extremely small) weakly universal machines very useful.

Problems we care only about a finite portion of the tape, which makes the Show that it is NP-hard to find an initial configuration (hand of cards) that If you are trying to make a (1-player) game this might be useful, for example to Input $w$ and time bound $t$ in unary, does $M$ accept $w$ within time $t$?) is P-complete. This implies that their prediction problem (given a machine $M$, Note that it is now known that all of the smallest universal Turing machines run It sounds like the (2,18) is most useful for you. Universal machine mentioned by David Eppstein. Word $r$ repeated infinitely to the right, with another constant word Here we have a single tape containing the finite input, and a constant (independent of the input) Here we have the usual notion ofīlank symbol in one or both directions of a single tape.Ĥ-symbol weakly universal machine (Neary, Woods 2009.

There is a 2-state, 18-symbol standard universal machine.

Model and here are two results that are of relevance to this Smallest known universal Turing machine depends on the details of the There have been some new results since the work cited in the previousĭescribes the state of the art (see Figure 1). It seems the (2,3) machine requires an initial state of tape that's nonperiodic, which will be a bit difficult to simulate within the rules of a card game. If the (2,3) machine isn't widely accepted as universal, what's the smallest N such that a (2,N) machine is noncontroversially accepted as universal?Įdited to add: It'd also be useful to know any requirements for the infinite tape for mentioned machines, if you happen to know them.

Is the (2,3) machine generally regarded as universal, non-universal, or controversial? I don't know where would be reputable places to look to find the answer to this. However, it seems (admittedly based on Wikipedia) that there's some controversy as to whether the (2, 3) machine is actually universal.įor rigour's sake, I'd like my proof to feature a "noncontroversial" UTM. So far I've created a game state which encodes Alex Smith's 2-state, 3-symbol Turing machine. I'd like to make it a universal Turing machine in order to prove Turing completeness. I'm wanting to encode a simple Turing machine in the rules of a card game.