# Tagged Questions

a particular kind of mathematically-based technique for the specification, development and verification of software and hardware systems.

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### What is coinduction?

I've heard of (structural) induction. It allows you to build up finite structures from smaller ones and gives you proof principles for reasoning about such structures. The idea is clear enough. ...
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### Equivalence of Büchi automata and linear $\mu$-calculus

It's a known fact that every LTL formula can be expressed by a Büchi $\omega$-automaton. But, apparently, Büchi automata are a more powerful, expressive model. I've heard somewhere that Büchi automata ...
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### Algorithm to solve Turing's “Halting problem‍​”

"Alan Turing proved in 1936 that a general algorithm to solve the halting problem for all possible program-input pairs cannot exist" Can I find a general algorithm to solve the halting problem for ...
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### Path to formal methods

It is not uncommon to see students starting their PhDs with only a limited background in mathematics and the formal aspects of computer science. Obviously it will be very difficult for such students ...
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### Looking for a book that derives and constructs a model checking application

I am teaching myself program verification and am currently learning proof assistants. I have the book Handbook of Practical Logic and Automated Reasoning which gives the proofs necessary for the ...
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### Formal Verification of Functional Programs

So I've been interested in learning more about formal verification, and I've seen a lot of interesting things like ACSL and JML which are based on the concept of Hoare triples. My question is, that ...
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### Contracts for Java Bytecode

Introduction For a paper I need contracts, which are also referred to as Design by Contract (DbC)1, and conceptually go back to Hoare[2]. For my work I need to apply contracts to Java bytecode. The ...
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### How to implement simulation on two LTSs?

Does any one know how to implement the simulation relation on two labelled transition systems (LTS)? I know how to do it for branching bi-simulation. The signature refinement theorem is used for ...
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### Mathematical background for programming languages, compilers and formal methods in software engineering [closed]

Can you tell me what mathematical background (concrete themes) should I have for studying and doing some investigations (in future) in programming languages, compilers and formal methods in software ...
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### Rigorous Proof of Insertion Sort

Currently I self study CLRS book (Outside of any course, so I got no access to an instructor) And I am stuck proving Insertion Sort, The proof in CLRS book is not so formal. Here's the algorithm: <...
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### Anotation rules for while rule in deductive verification

I have been studying deductive verification of software lately, with weakest precondition, strongest postcondition, annotation calculus, and etc. I came across the following rules for the while ...
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### How to Generate Control flow graph from a Petri net model?

My research is mainly focused on generating test sequences automatically using Colored Petri net.CFG provides techniques for generating test sequences. But some papers says that, test sequence ...
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### What does “post-image analysis” mean in the context of formal program analysis?

I am reviewing an anonymous paper about a sort of static analysis of programs that uses the phrase "post-image analysis", or "post-image operation" without defining what that is. I am guessing it is a ...
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### Language independent software libraries

When trying to decide on the choice of a programming language for a specific task, people will often tell me: "use this language because it has the best library for the type of problems you are ...
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### Witness for the $EU(\phi_1,\phi_2)$ using BDDs

I wanted ask if you know an algorithm to find the witness for $EU(\phi_1,\phi_2)$ (CTL formula "Exist Until") using BDDs (Binary Decision Diagram). In pratice you should use the fixed point for ...
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### Time to construct a GNBA for LTL formula

I have a problem with the proof for constructing a GNBA (generalized nondeterministic Büchi automaton) for a LTL formula: Theorem: For any LTL formula $\varphi$ there exists a GNBA $G_{\varphi}$ ...
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### What exactly is Symbolic Model Checking?

I know that Symbolic Model Checking is state space traversal based on representations of states sets and transition relations as formulas like in CTL using models like Kripke Model. I know the theory. ...
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### Initial Algebra example

If the definition of Initial Algebra is: "An object is initial if there exists a unique morphism from the object to every object in the category" Why do we need such object, and could any one give ...
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### Efficient algorithms for checking non-emptiness of the language of a Turing machine

I know that language non-emptiness is TM recognizable, and one can perform a BFS to find an input string that TM accepts, if there is any. But, what is the most efficient algorithm for that?
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### Regular Expressions with at least 2 0's and at most 1

I think the answer should be: $(1+ \epsilon)000^* + 0^*0(1+\epsilon)00^* + 000^*(1+\epsilon)$ But I am not sure if this is the right answer. Can someone explain the correct answer? And if it is ...
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### Logic applications and security protocols references request

I'm a student of logic and I'm interested in looking at logic applications, of which I am told there are many, in computer science and allied areas. I've seen some applications. More specifically, I ...
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### Questions from Dijkstra's EWD 1300: “The notational conventions I adopted, and why”

A link to the transcript of the manuscript: http://www.cs.utexas.edu/users/EWD/transcriptions/EWD13xx/EWD1300.html My questions: What does Dijkstra mean by: "Do not introduce priority [...
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### Trace dependents & precedents of a program in an imperative language

We have some programs in a very basic imperative language, the programs contain some basic features: assignment, condition, loop, scalar variables, 1-dimensional arrays and 2-dimensional arrays... ...
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### How to prevent deletion in an array in the B method

I have created a very basic model of an array list in the B method as shown below ...
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### How might I express a sequence of operations in formal terms?

I want to be able to represent a set of operations in sequential order such that they will represent what is traditionally called a "function" (which is not always the mathematical definition of a "...
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### Double ended queue data abstraction and axioms

I am trying to show the data abstraction for a double ended queue along with the axioms. A double ended queue is a queue where items can be added to and remove from either end of the queue. I have ...
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### Formalizing self-propagating behaviour

Since reading Ken Thompson's Reflections on Trusting Trust I am trying to formalize the idea of a program which mutates its own behaviour; specifically, a program that would be self-reproducing except ...