Waveform:-
I did a property as:
property p1;
a |=> (b == 1)[=2] ##1 (c == 1)[=2]
endproperty
But this property doesn't work well for this waveform, it isn't working for 3 or more "b's" before the "c's" and it isn't working for "c's" after the first "b".
I need a property that just can pass after the "a" signal just 2 "b's" and after just "2 c's" with any quantity of gaps between them.
thanks for help.
You do not specify that b should not be 1 when during the pulses on c, nor do you specify that c should not be 1 during the pulses on b.
So, how about something like this:
property p1;
a |=> ((c == 0) throughout (b == 1)[->2]) ##1 ((b == 0) throughout (c == 1)[->2]);
endproperty
The [->N] operator is the exact non-consecutive repetition operator or goto repetition operator. With goto repetition, the expression must hold in the final cycle of the match; in other words, the match is achieved as soon as the specified number of repetitions has occurred.
Related
def pos_neg(a, b, negative):
if negative:
return (a < 0 and b < 0)
else:
return ((a < 0 == b > 0) or (a > 0 == b < 0))
so basically I tried some basic problems.
I just started out and went to https://codingbat.com/prob/p162058 to try it and don't understand why if I were to replace the '==' with 'and' it would work? Thanks.
Oh, I got it now, thanks guys. :D
(this python community is fire!!!)
Since you're learning, you might be interested in seeing that this is an equivalent function.
basically it does a bit wise & and returns true if the result is < 0
else a bit wise exclusive or and returns true if the result is < 0
def pos_neg(a , b, negative):
if negative:
return (a & b) < 0 # both sign bits set (i.e. neg), return true
else:
return (a ^ b) < 0 # different signs, return true
In both cases, it is the sign bit of the result that is of concern. If the bit is set then the value will be negative (hence the comparison to < 0)
and is a logical operator and returns true only when both the expressions we are using it on are true.
== is used for comparisons and returns true when both expressions are equal; they don't need to be true.
To give you an example False == False will return True but False and False will return False.
This "==" means equals to, belonging to Python Comparison Operators, used to compare two values.
and language keyword "and" it is for Python Logical Operators used to combine conditional statements.
You should check out this, it may solve others doubts you have.
W3Schools
All your relational operator usages (i.e. a < 0, b < 0, etc.) result to a boolean value and thus these are known as boolean expressions.
When you put a < 0, think of it like a test of: "is a less than 0, true or false?".
So, if both a and b are negative (i.e. less than zero), their expressions will return true.
So on the line return a < 0 and b < 0, replacing and with == is like saying return true == true. Without the change it'd be return true and true.
Note: This does not mean == is the same as and. == checks for equality of the left-hand side to the right-hand side (e.g. 1 == 1) and gives a true or false value depending on the result of equality. and checks for if the left-hand side results to a true statement and if the right-hand side results to a true statement in order to result to a true expression.
I'm getting started with Promela, and I'm having trouble expressing some LTL formulas.
An example is the following sequence value that I'd like to assert is monotonically increasing. Intuitively I want to write that in the next state, sequence is >= its previous value, but looking through documentation, I don't see a way to express this. Is there a method for expressing this type of formula?
byte sequence = 0;
ltl p0 { [] sequence >= prev(sequence) }
... processes that manipulate sequence ...
Assuming that it's possible to express the monotonically increasing property of sequence above, I'm wondering if there is a syntax for wildcard array indexing. Similar to the above example, I intuitively want to reference all previous index entries.
byte values[N];
byte index = 0;
ltl p1 { values[0..index-1] are monotonically increasing }
... processes ...
Thanks a lot for your help. Promela seems really great :)
AFAIK,
Monotonically Non-decreasing Sequence.
Linear Temporal Logic has a X operator that allows one to express a property that refers to a boolean condition holding in the next state, as opposed to the previous state.
However, one cannot directly compare an integer value of the current state with that of the next state within an LTL formula, because X evaluates to a Boolean value.
In theory, what one can do is to encode the <= operator over the integer as a Boolean property by bit-blasting it, e.g. by means of some clever use of the modulo operator or bitwise operations (it should not be too hard with unsigned variables) and a bit-to-bit comparison of the corresponding Boolean values (see final note).
From a modeling point of view, however, the easiest approach is to enrich your model with a prev_value variable and simply check that in each state the property prev_value <= cur_value holds. Notice that in this case you should use the d_step command to group together the two value assignments, so that they are conflated within a single state with no intermediate transitions, e.g.
...
byte prev_value;
byte cur_value;
...
d_step {
prev_value = cur_value;
cur_value = ... non-blocking function ...
}
Otherwise, the invariant property relating prev_value to cur_value may result to be broken on the corresponding automaton for some state s_i. (note: this would actually not hinder the verification of the specific LTL property you are interested in, but it can be an issue with other formulas)
Wildcard Indexing.
If I understand correctly, you want to express a property s.t. --in each state-- only memory locations from 0 up to index-1 are required to be monotonically non-decreasing, with index being a variable which can change value (arbitrarily?).
The structure of such property should be:
ltl p1 {
[] (
((1 <= index) -> "... values[0] is monotonically non-decreasing ...") &&
((2 <= index) -> "... values[1] is monotonically non-decreasing ...") &&
((3 <= index) -> "... values[2] is monotonically non-decreasing ...") &&
...
((N <= index) -> "... values[N-1] is monotonically non-decreasing ...")
)
}
I believe the answer to your question is no. However, I suggest you to use macros for the C preprocessor to simplify the encoding of your properties and avoid writing the same things over and over again.
Note:
Let's take curr_int and next_int 0-1 Integer variables s.t. next_int is equal to the value of curr_int in the next state (aka, curr_int is the previous value of next_int), and a curr Boolean variable s.t. curr is true if and only if curr_int is equal to 1.
Then, by the LTL semantics, X curr is true if and only if curr_int (next_int) is equal to 1 in the next (current) state.
Consider the following truth-table for state s_i:
curr_int | next_int | curr_int <= next_int
0 | 0 | 1
0 | 1 | 1
1 | 0 | 0
1 | 1 | 1
From the above definitions, we can rewrite it as:
curr | X curr | EXPR
false | false | true
false | true | true
true | false | false
true | true | true
From the truth-table it's can be seen that EXPR corresponds to
!curr v (X curr)
which can be more elegantly rewritten as
curr -> (X curr)
Thich is our final LTL-encodeable version of curr_int <= next_int for a given state s_i, when both are 0-1 Integer variables.
There is no such symbol in Promela. Yet any Past Time LTL formula can be translated into Future Time LTL (probably even more cumbersome one).
Not sure though is there an easy way to compare values of variables in different states.
Also check LTL specification pattern repository for past.
See discusssion in CS stackexhange
https://cstheory.stackexchange.com/questions/29444/do-past-time-ltl-and-future-time-ltl-have-the-same-expressiveness
in designing an algebraic equation modelling system, I had this dilemma: we cannot associate properties to a number, if I turn the number to a table with a field "value" for example, I can overload arithmetic operators, but not the logic operator since that only works when both operands have same metatable, while my users will compare "x" with numbers frequently.
For example, here is a minimal equation solver system:
x = 0
y = 0
eq1 = {function() return 2*x + 3*y end, rhs = 1 }
eq2 = {function() return 3*x + 2*y end, rhs = 2 }
p = {{x,y},{eq1, eq2}}
solve(p)
The "solve()" will process table "p" to get all coefficients of the equation system and rhs. However, it is essential, a user can associate properties to "x" and "y", for example, lower bound, upper bound. I tries using table,
x = {val=0, lb=0, ub=3}
y = {val=1,lb=3,ub=5}
....
and write metamethods for "x" and "y" such that arithmetic operating will act on x.val and y.val. However, in a scripting environment, we also need to compare "x" with numbers, i.e., "if x>0 then ...". And I stuck here. An ugly solution is to ask users to use x.val, y.val everywhere in modelling the equation and scripting. Does anyone here has similar need to associate properties to a number, and the number can still be used in arithmetic/logic operations?
Something like this could work:
x = {val = 10}
mt = {}
mt.__lt = function (op1, op2)
if (type(op1) == 'table') then a = op1.val else a = op1 end
if (type(op2) == 'table') then b = op2.val else b = op2 end
return a < b
end
setmetatable(x, mt)
print(x < 5) -- prints false
print(x < 15) -- prints true
print(x < x) -- prints false
print(5 < x) -- prints true
Of course, you would write similar methods for the other operators (__add, __mul, __eq and so on).
If you'd rather not use type()/reflection, you can use an even dirtier trick that takes advantage of the fact that unary minus is well, unary:
mt = {}
mt.__unm = function (num) return -(num.val) end
mt.__lt = function (a, b) return -(-a) < -(-b) end
This is rather simple if you have access to the debug library, do you?
debug.setmetatable(0, meta)
meta will be the metatable of ALL numbers. This will solve your logical overloading problem.
However if you would prefer assigning properties to numbers, there is a way you could do this, I wrote a quick example on how one would do so:
local number_props = {
{val="hi"},
{val="hi2"}
}
debug.setmetatable(0,{__index=function(self,k)return number_props[self][k]end})
print((1).val, (2).val)
i dont understand why the code bellow doesnt work properly. If both variables a and b < 0 it should print that both numbers are negative,else the last message. But it just dont work so, what am i doing wrong? please help!
import random
while True:
input()
a=random.randint(-9,9)
b=random.randint(-9,9)
print(a,b)
if a and b < 0:
print("2 negative numbers:",a,b)
else:
print("one or both of the numbers are positive!")
I'm running this on python 3.4.
I think you're a little confused about how operators distribute.
When you have
if a and b < 0
it doesn't mean
if (both a and b) < 0
but instead
if (a) and (b < 0)
which is equivalent to
if (a != 0) and (b < 0)
since "numeric zero of all types ... evaluates to false" (see the reference on booleans on docs.python.org)
Instead, you want
if a < 0 and b < 0
which will tell you if both a and b are less than zero.
Evaluating Both Operands will resolve the issue. Here both Operands are expressions which results in true or false, so if both result in true; you will get your required result.
if ((a < 0) and (b < 0)):
You are evaluating just a, not it's relation to 0:
if a < 0 and b < 0:
This:
a and b < 0:
Is equivalent to this:
(a) and (b < 0):
(a) is False when a equals 0 and True otherwise. Therefore, due to short-circuiting b < 0 isn't even evaluated.
As a fix you may use all method:
all(i < 0 for i in (a, b))
protected int xMethod (Integer a, Integer b) {
if (a<b)
return 1
else if (a>b)
return 2
else
return 3
}
I wonder if there is some way of rewriting above method differently in groovy? as now is very Java style.
It seems that the function just needs to return 3 different values depending on whether a is less than, equal to, or greater than b. There is already an operator in Groovy that does this:
a <=> b
The return values are -1, 0 and 1. Perhaps the best thing to do is refactor the code to use this operator instead of xMethod, if that is possible.
Of course, if the precise values 1, 2 and 3 are important and not just 3 distinct values then you can't do this.
Just to expand on Mark's answer:
protected int xMethod (Integer a, Integer b) {
switch ( a <=> b ) {
case -1: 1; break
case 1: 2; break
case 0: 3; break
}
}
However, you have to question whether this method has any value. If the caller can be changed to accept -1, 0, 1 then the method has no reason to exist.
How about:
return (a <=> b) + 2
If you remove the two occurrences of Integer from the signature, you can call the method with any parameters for which < is defined.
E.g.
assert x.xMethod(1, 2)==1
assert x.xMethod("2", "1")==2
assert x.xMethod(2.0, 2.0)==3