I am tasked with creating a small program that can read in the definition of a FSM from input, read some strings from input and determine if those strings are accepted by the FSM based on the definition. I need to write this in either C, C++ or Java. I've scoured the net for ideas on how to get started, but the best I could find was a Wikipedia article on Automata-based programming. The C example provided seems to be using an enumerated list to define the states, that's fine if the states are hard coded in advance. Again, I need to be able to actually read the number of states and the definition of what each state is supposed to do. Any suggestions are appreciated.
UPDATE:
I can make the alphabet small (e.g. { a b }) and adopt other conventions such as the
start state is always state 0. I'm allowed to impose reasonable restrictions on the number of
states, e.g. no more than 10.
Question summary:
How do I implement an FSA?
First, get a list of all the states (N of them), and a list of all the symbols (M of them). Then there are 2 ways to go, interpretation or code-generation:
Interpretation. Make an NxM matrix, where each element of the matrix is filled in with the corresponding destination state number, or -1 if there is none. Then just have an initial state variable and start processing input. If you get to state -1, you fail. If you run out of input symbols without getting to the success state, you fail. Otherwise you succeed.
Code generation. Print out a program in C or your favorite compiler language. It should have an integer state variable initialized to the start state. It should have a for loop over the input characters, containing a switch on the state variable. You should have one case per state, and at each case, have a switch statement on the current character that changes the state variable.
If you want something even faster than 2, and that is sure to get you flunked (!), get rid of the state variable and instead use goto :-) If you flunk, you can comfort yourself in the knowledge that that's what compilers do.
P.S. You could get your F changed to an A if you recognize loops etc. in the state diagram and print out corresponding while and if statements, rather than using goto.
One non-hardcoded way to represent an automaton is as a transition matrix, which allows to represent for each current state, and each input character, what the next state is.
You haven't actually asked a question. You'll get more and better help if you have a specific question for a specific task (but still give the overall goal). The question should be narrow in scope (e.g. not "How can I implement an FSA?").
As for how to represent an FSA (which seems to be what you're having difficulties with), read on.
Start by considering the definition of an FSM: it's an alphabet ∑, a set of states S, a start state s0, a set of accept states A and a transition function δ from a state and a symbol to a state. You have to be able to determine these properties from the input. Any states not reachable by the transition function can be dropped to produce an equivalent FSM. The minimal set of states and alphabet are thus implicit in the transition function; you could make your FSM easier to use (and harder to implement, but not much harder) by not requiring either ∑ or S in the input.
You don't need to use the same representation for states that the input uses. You could use unsigned integers for your internal representation, as long as you have a map from integers to strings and strings to integers so you can convert between the internal representation and external representation. This way, your transition function can be stored as an array, so the transition step can be performed in constant time.
A simpler approach would be to use the external representation as your internal representation. With this option, the transition function would be stored as a map from strings and symbols to strings. The transition step would probably be O(log(|S|+|∑|)), given the performance of most map data structures. If symbols are represented as integers (e.g. chars), the transition function could be represented as a map from strings to an array of strings, giving O(log(|S|)) performance.
Yet another optionmodeled after the graph view of an FSM, is to create a class for states. A state has a name (the external representation). States are responsible for transitions; send a symbol to a state and get back another state.
class State {
property name;
State& transition(Symbol s);
void setTransition(Symbol s, State& to);
}
Store the set of states as a map from names to states.
There you go, three different places to start, each with a different way to represent states.
Stop thinking about everything at once. Do one thing at a time
- come with language of state machine
- come with language for stimulus
- create sample file of one state machine in language
- create sample file of stimulus
- come with class for state
- come with class for transition
- come with class for state machine as set of states and transitions
- add method to handle violation to state class
- code a little parser for language
- code another parser for language
- initial state
- some output thing like WriteLn here and there
- main method
- compile
- run
- debug
- done
The way the OpenFst toolkit does it is: A FSM has a vector of states, each of which has a vector of arcs. Each arc has an input (and output) label, a target state ID and a weight. You could take a look at the code. Maybe it will inspire you.
If you're using an object-oriented language like Java or C++, I'd recommend that you start with objects. Before you worry about file formats and the like, get a good object model for a finite state automata and how it behaves. How will you represent states, transitions, events, etc.? Will your FSA be a Composite? Once you have that sort of thing working you can get the file formats right. Anything will do: XML, text, etc.
Related
I am trying to create a class that takes in a string input containing pseudocode and computes its' worst case runtime complexity. I will be using regex to split each line and analyze the worst-case and add up the complexities (based on the big-O rules) for each line to give a final worst-case runtime. The pseudocode written will follow a few rules for declaration, initilization, operations on data structures. This is something I can control. How should I go about designing a class considering the rules of iterative and recursive analysis?
Any help in C++ or Java is appreciated. Thanks in advance.
class PseudocodeAnalyzer
{
public:
string inputCode;
string performIterativeAnalysis(string line);
string performRecursiveAnalysis(string line);
string analyzeTotalComplexity(string inputCode);
}
An example for iterative algorithm: Check if number in a grid is Odd:
1. Array A = Array[N][N]
2. for i in 1 to N
3. for j in 1 to N
4. if A[i][j] % 2 == 0
5. return false
6. endif
7. endloop
8. endloop
Worst-case Time-Complexity: O(n*n)
The concept: "I wish to write a program that analyses pseudocode in order to print out the algorithmic complexity of the algorithm it describes" is mathematically impossible!
Let me try to explain why that is, or how you get around the inevitability that you cannot write this.
Your pseudocode has certain capabilities. You call it pseudocode, but given that you are now trying to parse it, it's still a 'real' language where terms have real meaning. This language is capable of expressing algorithms.
So, which algorithms can it express? Presumably, 'all of them'. There is this concept called a 'turing machine': You can prove that anything a computer can do, a turing machine can also do. And turing machines are very simple things. Therefore, if you have some simplistic computer and you can use that computer to emulate a turing machine, you can therefore use it to emulate a complete computer. This is how, in fundamental informatics, you can prove that a certain CPU or system is capable of computing all the stuff some other CPU or system is capable of computing: Use it to compute a turing machine, thus proving you can run it all. Any system that can be used to emulate a turing machine is called 'turing complete'.
Then we get to something very interesting: If your pseudocode can be used to express anything a real computer can do, then your pseudocode can be used to 'write'... your very pseudocode checker!
So let's say we do just that and stick the pseudocode that describes your pseudocode checker in a function we shall call pseudocodechecker. It takes as argument a string containing some pseudocode, and returns a string such as O(n^2).
You can then write this program in pseudocode:
1. if pseudocodechecker(this-very-program) == O(n^2)
2. If True runSomeAlgorithmThatIsO(1)
3. If False runSomeAlgorithmTahtIsO(n^2)
And this is self-defeating: We have 'programmed' a paradox. It's like "This statement is a lie", or "the set of all sets that do not contain themselves". If it's false it is true and if it is true it false. [Insert GIF of exploding computer here].
Thus, we have mathematically proved that what you want is impossible, unless one of the following is true:
A. Your pseudocode-based checker is incorrect. As in, it will flat out give a wrong answer sometimes, thus solving the paradox: If you feed your program a paradox, it gives a wrong answer. But how useful is such an app? An app where you know the answer it gives may be incorrect?
B. Your pseudocode-based checker is incomplete: The official definition of your pseudocode language is so incapable, you cannot even write a turing machine in it.
That last one seems like a nice solution; but it is quite drastic. It pretty much means that your algorithm can only loop over constant ranges. It cannot loop until a condition is true, for example. Another nice solution appears to be: The program is capable of realizing that an answer cannot be given, and will then report 'no answer available', but unfortunately, with some more work, you can show that you can still use such a system to develop a paradox.
The answer by #rzwitserloot and the ones given in the link are correct. Let me just add that it is possible to compute an approximation both to the halting problem as well as to finding the time complexity of a piece of code (written in a Turing-complete language!). (Compare that to the existence of automated theorem provers for arithmetic and other second order logics, which are undecidable!) A tool that under-approximated the complexity problem would output the correct time complexity for some inputs, and "don't know" for other inputs.
Indeed, the whole wide field of code analyzers, often built into the IDEs that we use every day, more often than not under-approximate decision problems that are uncomputable, e.g. reachability, nullability or value analyses.
If you really want to write such a tool: the basic idea is to identify heuristics, i.e., common patterns for which a solution is known, such as various patterns of nested for-loops with only very basic arithmetic operations manipulating the indices, or simple recursive functions where the recurrence relation can be spotted straight-away. It would actually be not too hard (though definitely not easy!) to write a tool that could solve most of the toy problems (such as the one you posted) that are given as homework to students, and that are often posted as questions here on SO, since they follow a rather small number of patterns.
If you wish to go beyond simple heuristics, the main theoretical concept underlying more powerful code analyzers is abstract interpretation. Applied to your use case, this would mean developing a mapping between code constructs in your language to code constructs in a different language (or simpler code constructs in the same language) for which it is easier to compute the time complexity. This mapping would have to conform to some constraints, in particular, the mapped constructs have have the same or worse time complexity as the original code. Actually, mapping a piece of code to a recurrence relation would be an example of abstract interpretation. So is replacing a line of code with something like "O(1)". So, the task is just to formalize some of the things that we do in our heads anyway when we are analyzing the time complexity of code.
1.What data structure to use for electric circuit representation
for Kirchoff Rules computation purposes
how to differentiate between different types of electric components
how to 'recognize' wire inter-connections between them
2.how to implement Kirchoff Rules
how to obtain current and voltage loops
how to store and evaluate Kirchoff equations
[original question text]
Specifically, how would the program recognize something is in series and parallel and how will it differentiate between a battery, resistor, capacitor, inductors, etc..
Java's an object-oriented language. Start thinking about how you'd model your system as objects.
You have a few object candidates already:
Battery
Resistor
Capacitor
Inductor
These would have input and output nodes. The output from one is the input to the next.
What about transistors? You'll have more than one input. What then? Those are non-linear. How do you model those?
You'll build in the proper behavior for each one and wire them together.
You'll have some kind of transient forcing function here. Input current or voltage waveforms. Output is current and voltage at each node versus time.
This is the electrical engineer's equivalent of finite element analysis.
These are really transient ODE, right? How do you plan to solve them? Numerical integration?
agree with duffymo's answer just some things to add (I am C++ friendly so I stick to it)
first some data to represent components
struct pin
{
char name[]; // name id for pin ("C","B","E"...
int part_ix,pin_ix; // connected to patrs[part_ix].pins[pin_ix]
double i,u; // actual: current,voltage
int direction; // in,out,bidirectional
};
struct part
{
char name[]; // name id for part ("resistor","diode",...
pin pins[n]; // n pins of the part (resistor has 2 , transistor has 3, ...)
// here add all values you need for simulation like:
double R,H21E,...
// or even better do a matrix for it so when you multiply it by input currents and voltages
// of every pin you get the correct currents and voltages
double m[n][n+n];
};
also you can add list of pins connections instead of part_ix,pin_ix to save some processing time.
circuit
part parts[];
simple dynamic list of components the interconnections are inside it
loops
you have to extract closed circuit loop from interconnections for current equations and get nodes that connect current loops for voltage equations. This would lead you to system of equations. Nodes have more that 2 connections and closed current loops are just sequence of connections leads back to itself. Look here:
https://stackoverflow.com/a/21884021/2521214
it is one of my answers where part of the code finds closed loops
evaluation
can use gauss elimination for that. Problematic are non linear components like diodes, transistors ... so may be you will need to add more matrices (approximate to polynomial with bigger degree) then you will need to multiply by all currents and voltages powered by (0,1,2,3,...). I think ^3 will be enough for most components and do not forget that some non linear component also need to remember their states (or last current,voltage,... ...).
Also sometimes is better to use symbolic expressions instead of matrix approach but for that you will need expression evaluation engine. I use this approach a lot for self resizing geometry in CAD/CAM meshes.
Hy,
Lets say you have Varchar-Database values in a column that are cAmeLCaSe and you always want to display them UPPERCASE in a view.
Is it now better to select those entrys using the (for example) UPPER-Function of Oracle
or to loop the results and call the .toUpperCase() Method from within the Java Code after the selection has been made?
I know its a bit of a general question and i will of corse comment after having made performance messurments of the above two possibilitys. But i am more after a good source of information that addresses such questions in general (like for example "is it better do run sorting db- side or in programm-code?" and questions like this for common Solutions like .Net/Java and Oracle/ MSSQL Server.
Many thanks you took the time to read this questions, i appreciate any input and wish you a great day.
Regards
Jan
It depends on where and how the uppercased value is used.
If this is only used in the frontend (I assume with "view" you did not mean a database view) then I'd go for a toUpperCase() ideally using the user's locale.
If you are using the uppercase value for comparison I'd use the Oracle function to ensure that the you have a consistent behaviour. I'm think of e.g. a condition where you compare the column value to a string constant: WHERE upper(foobar) = upper('SomeValue') If you used Java's toUpperCase() that might apply different (locale dependent) rules than Oracle would use.
I believe always my code should be database independent.
String upper = string.toUpperCase();
Because,it's database independent.If I shift my database to some other,I need not to change my code.
In a nutshell your specific requirements should take in to consideration.
The Title is self explanatory. This was an interview question. In java, List is an interface. So it should be initialized by some collection.
I feel that this is a tricky question to confuse. Am I correct or not? How to answer this question?
Assuming you don't have a copy of the original List, and the randomizing algorithm is truly random, then no, you cannot restore the original List.
The explanation is far more important on this type of question than the answer. To be able to explain it fully, you need to describe it using the mathematical definitions of Function and Map (not the Java class definitions).
A Function is a Map of Elements in one Domain to another Domain. In our example, the first domain is the "order" in the first list, and the second domain is the "order" in the second list. Any way that can get from the first domain to the second domain, where each element in the first domain only goes to one of the elements in the second domain is a Function.
What they want is to know if there is an Inverse Function, or a corresponding function that can "back map" the elements from the second domain to the elements in the first domain. Some functions (squaring a number, or F(x) = x*x ) cannot be reversed because one element in the second domain might map back to multiple (or none) elements in the first domain. In the squaring a number example
F(x) = x * x
F(3) = 9 or ( 3 -> 9)
F(12) = 144 or ( 12 -> 144)
F(-11) = 121 or (-11 -> 121)
F(-3) = 9 or ( -3 -> 9)
attempting the inverse function, we need a function where
9 maps to 3
144 maps to 12
121 maps to -11
9 maps to -3
Since 9 must map to 3 and -3, and a Map must have only one destination for every origin, constructing an inverse function of x*x is not possible; that's why mathematicians fudge with the square root operator and say (plus or minus).
Going back to our randomized list. If you know that the map is truly random, then you know that the output value is truly independent of the input value. Thus if you attempted to create the inverse function, you would run into the delimma. Knowledge that the function is random tells you that the input cannot be calculated from the output, so even though you "know" the function, you cannot make any assumptions about the input even if you have the output.
Unless, it is pseudo-random (just appears to be random) and you can gather enough information to reverse the now-not-truly random function.
If you have not kept some external order information (this includes things like JVM trickery with ghost copies), and the items are not implicitly ordered, you cannot recover the original ordering.
When information is lost, it is lost. If the structure of the list is the only place recording the order you want, and you disturb that order, it's gone for good.
There's a user's view, and there's internals. There's the question as understood and the question as can be interpreted.
The user's view is that list items are blocks of memory, and that the pointer to the next item is a set of (4?8? they keep changing the numbers:) bytes inside this memory. So when the list is randomized and the pointer to the next item is changed, that area of memory is overriden and can't be recovered.
The question as understood is that you are given a list after it had been randomized.
Internals - I'm not a Java or an OS guy, but you should look into situations where the manner in which the process is executed differs from the naive view: Maybe Java randomizes lists by copying all the cells, so the old list is still kept in memory somewhere? Maybe it keeps backup values of pointers? Maybe the pointers are kept at an external table, separate from the list, and can be reconstructed? Maybe. Internals.
Understanding - Who says you haven't got an access to the list before it was randomized? You could have just printed it out! Or maybe you have a trace of the execution? Or who said you're using Java's built it list? Maybe you are using your own version controlled list? Or maybe you're using your own reversable-randomize method?
Edwin Buck's answer is great but it all depends what the interviewer was looking for.
Alright, i have an assignment and i dont know how to parse the file. Is string tokenizer my best option?
The file has commas, newlines and spaces. S is the starting state and small a is the input and the big A is the next state. Should i parse the file into seperate variables and run it through a switch case to simulate a state machine?
This is the file
‘Ends in a
2
S, a, A
S, b, S
A, a, A
A, b, S
F: A
aba
bbaabba
bbabab
aaaab
b
a
Thank you so much because i just cant seem to get started...
My biggest question is how can i parse the file?
Like any other text file. There are literally millions of examples on how to do this on the web.
I would look for examples using the Scanner class.
I am not very good at parsing files. Especially in this situation.
With practice it will get easier. Doing this assignment will help.
Should i use dilimeters?
The file has delimiters so I don't why you wouldn't.
comma and newline?
Your file has commas, newlines and spaces.
and put the states into an array and the inputs ( a,b) into a second array?
Java is an object orientated programming language. Perhaps using Collections like Map and Objects is a better choice.
Should i check for digits, isaplha?
I would just assume the file is formatter correctly and read numbers when you expect to have a number and strings when you expect to have a word/token.
lower case and uppercase alpha?
Not sure if this is a consideration.
i am thinking i need a switch and a couple of cases to handle the state transitions?
If your states were handled in Java code, I would say yes. However you states are being read from a text files and stored in a data structure. In this case its simpler not to use switches.
Can someone explain how i should go about handling this file so i can process it?
Read it, store the data in a structure, process the inputs.
I am also confused on how to handle the :F A in that file..
This is information you need to record to determine when your DFA stops.
Java is an object-oriented language so build a series of classes that reflect the real world.
Example:
What do you have? And what do they need to be able to do
DFA
has a series of states
needs to be able to accept/reject input strings
State
has a collection of inputs to look for and states to transition to based on input
needs to be able to check for a token and transition to a new state
So these kind govern how you should lay out your classes (members and methods). So you should make a DFA class and it should have a method: public boolean process(String input).