XOR, AND Tree in Neo4j Cypher - neo4j

I have a problem trying to "decypher" a logical tree with Neo4js Cypher.
I have a logical tree of Operation to Leaves. I want to collect valid sets of Leaves.
I am currently trying to collect valid Sets of Leaves on a Valid Configuration Node. So I can later quickly path through that Configuration node.
Example
(1 AND 2) AND (3 AND 4)
Is easy to match (rule)-[AND*]->(leaf) return collect(leaf)
However
(1 XOR 2) AND (3 XOR 4)
Is a problem because whenever I collect 1,2,3,4 in a single variable, I cannot later properly get the cartesian product of the AND Operation. (13,14,23,24) would be valid.
In general I have a tree of variable depth (upto max about 3-4)
Operations are XOR, AND, Not AND, Not XOR
Is there a simple way in Cypher I am missing for navigating such trees?
Is trying to merge Valid Sets in a ValidConfiguration Node a good idea for fast Queries?
Later it should support a query of the form
(:Model)->(:ValidConf)->(:Leaf:Option)->(:Feature)
then return all models that have a certain Feature in a valid configuration.
Or multiple Features at a certain configuration price.
Do I need UDFs or ObjectGraphMapper to get this problem solved?
Are there any UDFs that work with such decision trees which I can use?
Any help would be highly appreciated.
Create Example
CREATE (r:Rule{id:123})-[:COMPOSITION]->
startOp:AndOperation:Operation:Operand)
CREATE (startOp)-[:AND]->(intermediateOp1:OrOperation:Operation:Operand)
CREATE (startOp)-[:AND]->(intermediateOp2:OrOperation:Operation:Operand)
CREATE (intermediateOp1)-[:XOR]->(o1:Option:Operand{id:321})
CREATE (intermediateOp1)-[:XOR]->(o2:Option:Operand{id:564})
CREATE (intermediateOp2)-[:XOR]->(o3:Option:Operand{id:876})
CREATE (intermediateOp2)-[:XOR]->(o4:Option:Operand{id:227})
CREATE (o1)-[:CONSISTS_OF]->(f1:Feature{text:"magicwand"})
....
This tree is symmetric but they usually aren't. I need to make o1 + o4 be valid and o1 + o2 to not be valid. The OR are to be understood as XOR.

I don't think Cypher is going to work for evaluating a boolean binary expression tree. To quote cybersam's answer to a related question:
This is because Cypher has no looping statements powerful enough to
iteratively calculate subresults (in the correct order) for trees of
arbitrary depth.
You're going to have to look for some additional system to do the evaluation.
If you can code Java, you should be able to do this by implementing your own custom procedure to evaluate a boolean expression tree in the correct order.

Related

simplify equations/expressions using Javacc/jjtree

I have created a grammar to read a file of equations then created AST nodes for each rule.My question is how can I do simplification or substitute vales on the equations that the parser is able to read correctly. in which stage? before creating AST nodes or after?
Please provide me with ideas or tutorials to follow.
Thank you.
I'm assuming you equations are something like simple polynomials over real-value variables, like X^2+3*Y^2
You ask for two different solutions to two different problems that start with having an AST for at least one equation:
How to "substitute values" into the equation and compute the resulting value, e.g, for X==3 and Y=2, substitute into the AST for the formula above and compute 3^2+3*2^2 --> 21
How to do simplification: I assume you mean algebraic simplification.
The first problem of substituting values is fairly easy if yuo already have the AST. (If not, parse the equation to produce the AST first!) Then all you have to do is walk the AST, replacing every leaf node containing a variable name with the corresponding value, and then doing arithmetic on any parent nodes whose children now happen to be numbers; you repeat this until no more nodes can be arithmetically evaluated. Basically you wire simple arithmetic into a tree evaluation scheme.
Sometimes your evaluation will reduce the tree to a single value as in the example, and you can print the numeric result My SO answer shows how do that in detail. You can easily implement this yourself in a small project, even using JavaCC/JJTree appropriately adapted.
Sometimes the formula will end up in a state where no further arithmetic on it is possible, e.g., 1+x+y with x==0 and nothing known about y; then the result of such a subsitution/arithmetic evaluation process will be 1+y. Unfortunately, you will only have this as an AST... now you need to print out the resulting AST in order for the user to see the result. This is harder; see my SO answer on how to prettyprint a tree. This is considerably more work; if you restrict your tree to just polynomials over expressions, you can still do this in small project. JavaCC will help you with parsing, but provides zero help with prettyprinting.
The second problem is much harder, because you must not only accomplish variable substitution and arithmetic evaluation as above, but you have to somehow encode knowledge of algebraic laws, and how to match those laws to complex trees. You might hardwire one or two algebraic laws (e.g., x+0 -> x; y-y -> 0) but hardwiring many laws this way will produce an impossible mess because of how they interact.
JavaCC might form part of such an answer, but only a small part; the rest of the solution is hard enough so you are better off looking for an alternative rather than trying to build it all on top of JavaCC.
You need a more organized approach for this: a Program Transformation System (PTS). A typical PTS will allow you specify
a grammar for an arbitrary language (in your case, simply polynomials),
automatically parses instance to ASTs and can regenerate valid text from the AST. A good PTS will let you write source-to-source transformation rules that the PTS will apply automatically the instance AST; in your case you'd write down the algebraic laws as source-to-source rules and then the PTS does all the work.
An example is too long to provide here. But here I describe how to define formulas suitable for early calculus classes, and how to define algebraic rules that simply such formulas including applying some class calculus derivative laws.
With sufficient/significant effort, you can build your own PTS on top of JavaCC/JJTree. This is likely to take a few man-years. Easier to get a PTS rather than repeat all that work.

storing decision tree in neo4j

I've been looking for a way to 'productionize' R or python based Random Forest/Gradient boosting tree models, and had thought that since all the individual component decision tree are binary trees, exporting to a graphical database might be a workable solution (deploying by holding the models in memory and invoking from a lightweight restful library like Flask doesn't scale that well). Here's how a decision tree is normally traversed:
1.) Data gets passed to the root node
2.) We check if the present node is a leaf node; if it is, we return a set of attributes (the predicted distribution/value).
If not, the node stores a decision rule, and checks the relevant column for which node to pass the data to next (e.g., "If age>9.5, move to left node")
Repeat 2-3.
I'm new to neo4j and graph databases in general, and it wasn't clear to me that it is possible to store(and subsequently traverse) decision rules in a node; all the examples I saw tended to be in the vein of
MATCH (neo:Database {name:"Neo4j"})
MATCH (johan:Person {name:"Johan"})
CREATE (johan)-[:FRIEND]->(:Person:Expert {name:"Max"})-[:WORKED_WITH]-> (neo)
where the conditional statements are prespecified in a query. Is this something which is feasible with neo4j, and if so, which areas of the documentation should I be focusing on?
Thank you for any guidance you could provide.
Interesting problem.
You need a way to export a model out of R or Python and translate that into a Neo4J graph.
The export mechanism can be PMML (if you're using R rpart package to generate prunded trees), Google protobuf (if you're using R gbm package to generate trees), or simply an Excel spreadsheet.
Parsing and unmarshalling to Neo4J is your issue.
I am not affiliated with Yhat in any way, but reading your question made me think of an alternative approach.
Yhat Science Ops
I don't know what that means for your team internally, but it seems like a pretty simple way to have a model easy to call via a basic API call.

Source code logic evaluation

I was given a fragment of code (a function called bubbleSort(), written in Java, for example). How can I, or rather my program, tell if a given source code implements a particular sorting algorithm the correct way (using bubble method, for instance)?
I can enforce a user to give a legitimate function by analyzing function signature: making sure the the argument and return value is an array of integers. But I have no idea how to determine that algorithm logic is being done the right way. The input code could sort values correctly, but not in an aforementioned bubble method. How can my program discern that? I do realize a lot of code parsing would be involved, but maybe there's something else that I should know.
I hope I was somewhat clear.
I'd appreciate if someone could point me in the right direction or give suggestions on how to tackle such a problem. Perhaps there are tested ways that ease the evaluation of program logic.
In general, you can't do this because of the Halting problem. You can't even decide if the function will halt ("return").
As a practical matter, there's a bit more hope. If you are looking for a bubble sort, you can decide that it has number of parts:
a to-be-sorted datatype S with a partial order,
a container data type C with single instance variable A ("the array")
that holds the to-be-sorted data
a key type K ("array index") used to access the container that has a partial order
such that container[K] is type S
a comparison of two members of container, using key A and key B
such that A < B according to the key partial order, that determines
if container[B]>container of A
a swap operation on container[A], container[B] and some variable T of type S, that is conditionaly dependent on the comparison
a loop wrapped around the container that enumerates keys in according the partial order on K
You can build bits of code that find each of these bits of evidence in your source code, and if you find them all, claim you have evidence of a bubble sort.
To do this concretely, you need standard program analysis machinery:
to parse the source code and build an abstract syntax tree
build symbol tables (ST) that know the type of each identifier where it is used
construct a control flow graph (CFG) so that you check that various recognized bits occur in appropriate ordering
construct a data flow graph (DFG), so that you can determine that values recognized in one part of the algorithm flow properly to another part
[That's a lot of machinery just to get started]
From here, you can write ad hoc code procedural code to climb over the AST, ST, CFG, DFG, to "recognize" each of the individual parts. This is likely to be pretty messy as each recognizer will be checking these structures for evidence of its bit. But, you can do it.
This is messy enough, and interesting enough, so there are tools which can do much of this.
Our DMS Software Reengineering Toolkit is one. DMS already contains all the machinery to do standard program analysis for several languages. DMS also has a Dataflow pattern matching language, inspired by Rich and Water's 1980's "Programmer's Apprentice" ideas.
With DMS, you can express this particular problem roughly like this (untested):
dataflow pattern domain C;
dataflow pattern swap(in out v1:S, in out v2:S, T:S):statements =
" \T = \v1;
\v1 = \v2;
\v2 = \T;";
dataflow pattern conditional_swap(in out v1:S, in out v2:S,T:S):statements=
" if (\v1 > \v2)
\swap(\v1,\v2,\T);"
dataflow pattern container_access(inout container C, in key: K):expression
= " \container.body[\K] ";
dataflow pattern size(in container:C, out: integer):expression
= " \container . size "
dataflow pattern bubble_sort(in out container:C, k1: K, k2: K):function
" \k1 = \smallestK\(\);
while (\k1<\size\(container\)) {
\k2 = \next\(k1);
while (\k2 <= \size\(container\) {
\conditionalswap\(\container_access\(\container\,\k1\),
\container_access\(\container\,\k2\) \)
}
}
";
Within each pattern, you can write what amounts to the concrete syntax of the chosen programming language ("pattern domain"), referencing dataflows named in the pattern signature line. A subpattern can be mentioned inside another; one has to pass the dataflows to and from the subpattern by naming them. Unlike "plain old C", you have to pass the container explicitly rather than by implicit reference; that's because we are interested in the actual values that flow from one place in the pattern to another. (Just because two places in the code use the same variable, doesn't mean they see the same value).
Given these definitions, and ask to "match bubble_sort", DMS will visit the DFG (tied to CFG/AST/ST) to try to match the pattern; where it matches, it will bind the pattern variables to the DFG entries. If it can't find a match for everything, the match fails.
To accomplish the match, each of patterns above is converted essentially into its own DFG, and then each pattern is matched against the DFG for the code using what is called a subgraph isomorphism test. Constructing the DFG for the patter takes a lot of machinery: parsing, name resolution, control and data flow analysis, applied to fragments of code in the original language, intermixed with various pattern meta-escapes. The subgraph isomorphism is "sort of easy" to code, but can be very expensive to run. What saves the DMS pattern matchers is that most patterns have many, many constraints [tech point: and they don't have knots] and each attempted match tends to fail pretty fast, or succeed completely.
Not shown, but by defining the various bits separately, one can provide alternative implementations, enabling the recognition of variations.
We have used this to implement quite complete factory control model extraction tools from real industrial plant controllers for Dow Chemical on their peculiar Dowtran language (meant building parsers, etc. as above for Dowtran). We have version of this prototyped for C; the data flow analysis is harder.

Comparing arrays elements in Erlang

I'm trying to learn how to think in a functional programming way, for this, I'm trying to learn Erlang and solving easy problems from codingbat. I came with the common problem of comparing elements inside a list. For example, compare a value of the i-th position element with the value of the i+1-th position of the list. So, I have been thinking and searching how to do this in a functional way in Erlang (or any functional language).
Please, be gentle with me, I'm very newb in this functional world, but I want to learn
Thanks in advance
Define a list:
L = [1,2,3,4,4,5,6]
Define a function f, which takes a list
If it matches a list of one element or an empty list, return the empty list
If it matches the first element and the second element then take the first element and construct a new list by calling the rest of the list recursivly
Otherwise skip the first element of the list.
In Erlang code
f ([]) -> [];
f ([_]) -> [];
f ([X, X|Rest]) -> [X | f(Rest)];
f ([_|Rest]) -> f(Rest).
Apply function
f(L)
This should work... haven't compiled and run it but it should get you started. Also in case you need to do modifications to it to behave differently.
Welcome to Erlang ;)
I try to be gentle ;-) So main thing in functional approach is thinking in terms: What is input? What should be output? There is nothing like comparing the i-th element with the i+1-th element alone. There have to be always purpose of it which will lead to data transformation. Even Mazen Harake's example doing it. In this example there is function which returns only elements which are followed by same value i.e. filters given list. Typically there are very different ways how do similar thing which depends of purpose of it. List is basic functional structure and you can do amazing things with it as Lisp shows us but you have to remember it is not array.
Each time you need access i-th element repeatable it indicates you are using wrong data structure. You can build up different data structures form lists and tuples in Erlang which can serve your purposes better. So when you face problem to compare i-th with i+1-th element you should stop and think. What is purpose of it? Do you need perform some stream data transformation as Mazen Harake does or You need random access? If second you should use different data structure (array for example). Even then you should think about your task characteristics. If you will be mostly read and almost never write then you can use list_to_tuple(L) and then read using element/2. When you need write occasionally you will start thinking about partition it to several tuples and as your write ratio will grow you will end up with array implementation.
So you can use lists:nth/2 if you will do it only once or several times but on short list and you are not performance freak as I'm. You can improve it using [X1,X2|_] = lists:nthtail(I-1, L) (L = lists:nthtail(0,L) works as expected). If you are facing bigger lists and you want call it many times you have to rethink your approach.
P.S.: There are many other fascinating data structures except lists and trees. Zippers for example.

Binary search in Erlang in lg(n) time

I was searching through the possible work arounds for doing Binary search in Erlang and I found http://ruslanspivak.com/2007/08/15/my-erlang-binary-search/ But I was wondering if the solution in blog runs in O(lg n). Now since the recurrence for Binary search is:T(n) = T(n/2) + c which gives me an execution time of O(lg n).
Since in a C array you have the power of accessing any element in O(1) time. But in erlang if accessing the middle of list takes cn time, then binary search runs in linear overall time as poor as linear search.
I came across lists:nth/2 BIF for finding the nth item in a list but I am not sure about its execution time.
Any comments ?
There are a few data structures that allow O(1) access in Erlang: ETS tables, tuples and binaries.
Now, none of them would really be appropriate for a binary search. The ETS table supports searching from the start, and otherwise, data is copied to your process when returning the result, which is likely not going to be optimal for your use case.
Tuples allow O(1) access with element/2, but modifying them has a certain overhead (which is why the array module uses trees of tuples).
Then you have binaries (<<1,2,3,4,5>>), which allow for something similar to pointer arithmetic, like in the following example:
1> Sorted = <<$a,$b,$c,$d,$e,$f,$g,$h>>.
<<"abcdefgh">>
2> <<_:3/binary, X:1/binary, _/binary>> = Sorted.
<<"abcdefgh">>
3> X.
<<"d">>
However, predicting the performance when building the binary is a bit sketchy, and this kind of pointer arithmetic is harder to do if your values have different types and different sizes when represented in a binary.
Your best bet would likely be to use a list of values, sort it, then use list_to_tuple/1 to navigate around it with element/2.
I would however strongly recommend using a tree to do your searching; it would likely be much much simpler to use the gb_tree module to build a balanced tree and still get O(log N) search.
nth is O(n). Use array module for constant access data structure (array as in C - almost).

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