How to make a Turing machine graph which recognizes all words with an even number of a's but which is not a decider and nothing else. Also, how to make a decider Turing machine graph for the same language.
The language of all words with an even number of a's is a regular language, so a simple two-state DFA will accept the language. The same machine is a two-state decider TM that happens not to use the tape for anything except reading input.
To turn such a decider into a recognizer-non-decider (since all deciders are recognizers, too) we must make the TM explicitly recognize strings with an odd number of a's and, rather than simply halt-reject, go into an infinite loop. This can easily be done with a single state.
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TLDR: I have an asymmetric evaluation function for an implementation of negamax - is that acceptable? Or do I need to make it symmetric?
Longer:
I'm writing a game AI (for the chess-like board game "Hive") that was using minimax with alpha-beta pruning and an asymmetric evaluation function.
But I was having trouble adding transposition tables correctly, and was losing confidence in my minimax implementation, so I decided to switch to negamax using the pseudo-code here: https://en.wikipedia.org/wiki/Negamax#Negamax_with_alpha_beta_pruning_and_transposition_tables
I've got everything "working" and AFAIK accurately following the pseudo-code, but my AI is now making some wildly different moves than before and games that usually ended after 10-15 turns now take 30+, and I'm not convinced the AI is actually playing better than it was before. I'm worried that having an asymmetric evaluation function means I'm scoring nodes differently than before (because of the negamax flip-flopping).
I don't want to change to a symmetric function unless I really have to - I've been trying to produce an optimal function experimentally (AI vs AI battles) and have put in hundreds if not thousands of compute hours into producing a strong evaluation function.
Negamax support asymmetric evaluation functions but it does not lead to optimal play (assuming you have no knowlege about your opponent).
I don't know enough about Hive, but in computer chess it is, in general, a bug to have an asymmetric evaluation function. The reasons behind it should be the same for chess and Hive.
For instance, take the starting position (in chess). White is next to move and let us assume your evaluation function gives the position a score of +0.08.
Now change the position, so black is first to move. Everything is the same, only that the roles of white and black has been changed. Under the assumption, that +0.08 was the optimal score for the white position, why should the position for black not also be evaluated as +0.08?
The same argument goes for any position. If you reverse everything, there is no good reason for playing the position differently.
There is only one exception to this rule. If one opponent is clearly stronger than the other, there are arguments for an asymmetric evaluation. For instance, take a completely drawn position like this:
FEN: 4k3/8/8/p1p1p1p1/PpPpPpPp/1P1P1P1P/8/4K3 b - - 0 1
This position could safely be evaluated as 0. Now imaging the starting position but white starts without one knight. This should be a strong advantage for black.
Let us assume you are Magnus Carlsen and you are playing against on opponent who does not even know the chess rules. Which position would you prefer? Here, I would argue that an asymmetric evaluation could make sense (e.g., evaluate a likely draw similar to a loss). Carlsen should avoid the drawn position, while the beginner should prefer it.
The chances that the beginner can hold its own against the world champion, even at one knight odds, are practically zero. On the other hand, in the drawn position, the skill advantage does not matter, as no order of moves can result in a win or loss.
In computer chess, Rebel had a function to prefer tactical positions when playing against humans (see ANTI GRANDMASTER PLAY). There is also the common concept of "contempt", which is the score that engines give for a remis.
But note that in both my examples, this is not optimal play. Magnus Carlsen would not choose the position without the knight when playing a strong (or unknown) opponent. Also Rebel would not use the anti-human strategy against other machines, which also excel in tactical battles. (Even though, depending on the position, Rebel 10 did use ANTI GRANDMASTER PLAY against computers.)
I want to know how to represent a coffee machine using a Deterministic finite automata?
I've tried a lot to do this job.
I represented each and every processes as a set,by putting one to one correspondence with Natural numbers.
But I still don't know how to represent it using DFA.
First, try to imagine the states your automaton can be in. Something like:
Off, Ready, Working
Afterwards imagine the buttons or inputs you have to perform to switch between these states. Do not forget to define every input on every state. If you leave out several transitions, the automaton is not deterministic therefore is an NFA. Transitions could be:
0 for power off/on
1 for start/stop working
Off -0-> Ready
Ready -1-> Working
Ready -0-> Off
Working -1-> Ready (4 for the actual working process)
Off -1-> Off
Working -0-> Working (nothing happens in this cases)
Just connect the states with the given transitions, and voilá!
How could I show that there exist infinitely many DFA's each of which recognises the language {ϵ,a,b}.
That depends on how you are counting DFAs. Clearly there is one DFA for the language, and you can always add an unreachable state to the automaton. Ordinarily, though, such trivial differences are discounted, and with a finite language, there are only a finite number of different DFAs. With an infinite language there would be cycles in the transition graph which can be expanded again and again, which makes for a more significant difference. Another way to put it, you cannot show that there exist an infinite number of different DFAs for the given finite language.
I'm looking for a way to write a program that creates short german sentences with a restricted letter set. The sentences can be nonsense but should grammatically be correct. The following examples only contain the letters "aeilmnost":
"Antonia ist mit Tina im Tal."
"Tamina malt mit lila Tinte Enten."
"Tina nimmt alle Tomaten mit."
For this task I need a dictionary like this one (found in the answer to "Where can I find a parsable list of German words?"). The research area for programatically create text is NLG - Natural Language Generation. On the NLG-Wiki I found a large table of NLG systems. I picked two from the list, which could be appropriate:
SimpleNLG - a Java API, which has also an adaption for the german language
KOMET - multilingual generation, from University Bremen
Do you have worked with a NLG library and have some advice which one to use for building short sentences with a letter set restriction?
Can you recommend a paper to this topic?
Grammatically correct is a pretty fuzzy area, since grammar is not to strictly defined as one might think. What you really want here though, is a part-of-speech tagger, and a markov chain.
Specifically a markov chain says that given a certain state (the first word for instance) there's just a certain chance of moving on to another state (the next word). They are relatively easy to write from scracth, but I've got a gist here in python that shows how they work if you want an example.
Once you've got that I would suggest a part-of-speech-based markov chain, combined with just checking to see if words are constructed from your desired character set. In general the algorithm would go something like this:
Pick first word at random, checking that it is constructed solely from your desired set of characters
Use the Markov Chain to predict the next word
Check if that word is an appropriate part of speech, and that it conforms to the desired character set.
If not, predict another word until it is the case.
If so, then repeat starting at 2 to completion.
Hope that's what you're looking for. Let me know if you have any more questions.
As Slater Tyranus already said, Markov chains certainly form the basis of this task. I am going to suggest a more heavy-duty approach. It is considerably more work, but is likely to give much better results in terms of grammatical correctness.
Language Model based on PCFG parse trees: A language model works by assigning a probability to a sequence of words. It requires training data, however, in order to be built first. In your case, the training process should disregard words containing letters outside the limited set.
While theoretically a language model based on parse trees is much more likely to serve your purpose, there is one caveat: due to the kind of letter-based restriction you have, data sparsity will certainly raise its ugly head. Backoff techniques (e.g. Katz's backoff model) can help a bit, but it will essentially depend on whether or not you can train on enough enough data.
As far as readily available parsers are concerned, the Stanford NLP group provides a German parser based on the Negra corpus, as mentioned in their home page.
Im am working on a VHDL project that includes an fsm.
Some states change according to a counter. It dit not work until i put 'clk' in the sensitivity list, besides the current state and the input.
I know that during synthesis, the sensitivity not used, or discarded. But how can that have such an impact on the result in the simulation? if a leave this 'clk', would the fsm perform as i want op an FPGA?
thanks,
David
This is the simple explanation:
The simulator uses the sensitivity list to figure out when it needs to run the process. The reason why the simulator needs hints to figure out when to run the process is because computer processors can only do one (or only a few in multicore systems) thing at a time and the processor will have to take turns running each part of your design. The sensitivity list allows simulation to run in a reasonable time frame.
When you synthesize code into an ASIC or FPGA, the process is always "running" since it has dedicated hardware.
When you simulate a state machine without the clock in the sensitivity list, the process will never run on the clock edges, but only on changes to your input. If you have the state transition implemented as a flip flop (if clk'event and clk = '1') then your state transition will never be simulated unless you happen to change your input at the same time as the clock's rising edge.
You should probably leave the clock in the sensitivity list, assuming the FSM changes on clock edges.
Also, try to proofread your questions.
Synthesis tools focus on logic design (FPGA, ASIC) and ignore sensitivity lists because there are only three basic types of logic: Combinational logic, edge sensitive storage (flip-flops and some RAM), and level sensitive storage (latches and some RAM).
Combinational logic requires all input signals to be on the sensitivity list. From a synthesis tool perspective, if one is missing, they can either ignore the sensitivity list and treat it as if all inputs were on the sensitivity list, or produce some complicated combination of flip-flops and combinational logic that probably will not do what the user wanted anyway. Both of these have an implementation cost to the vendor, hence, why invest money (development time) to create something that is not useful. As a result, the only good investment is to simplify and ignore the sensitivity list.
Simulators on the other hand, have a bigger perspective than just logic design. The language defines sensitivity lists as to indicate when the code should run. So simulators implement that semantic with a high fidelity.
Long term it may make you happy to know that VHDL-2008 allows the keyword "all" to be used in a sensitivity list to replace the signal inputs there. This is intended to simplify the modeling of combinational logic. Syntax is as follows:
MyStateMachine : process(all)
begin
-- my statemachine logic
end process MyStateMachine ;
Turn on the VHDL-2008 switch and it out in your synthesis tool. If it does not work, be sure to submit a bug against the tool.