Several software verification competitions have been organized last years, with different objectives and modalities. Some problems from these competitions have been selected and solved using the B method. For each of these problems, are provided:
- a B model archive, containing the B models, the proof files (saved demonstration), the added mathematical rules (to be used during interactive proof)
- a report:
- explaining how the problem was tackled (possibly with several options), how the proof was conducted,
- providing project metrics per component
- showing the generated source code when executed
- source code, generated by Atelier B from B models and handwritten for others files.
These projects should be replayed with Atelier B 4.1.0 with the parameters below. Copy the two lines, select your Atelier B project, open contextual menu, select “properties” then “resources file”, paste the two lines at the end of the file, press “OK”.
Problem 1: Sum and maximum
“Given an N-element array of natural numbers, write a program to compute the sum and the maximum of the elements in the array.”
Problem 2: Inverting an injection
“Invert an injective array A on N elements in the subrange from 0 to N-1, i.e. the output array B must be such that B[A[i]] = i for 0 ≤ i ˂ N. You can assume that A is surjective.”
Problem 3: Searching a Linked List
“Given a linked list representation of a list of integers, find the index of the first element that is equal to 0.”
Problem 4: N-Queens
“Write a program to place N queens on an N*N chess board so that no queen can capture another one with a legal move.”
The COST IC701 Verification Competition 2011 was organized at the occasion of the conference on Formal Verification of Object-Oriented Software, held in 5-7 October, 2011, at Turin, Italy (website). Problems are available here.
Challenge 3: Two equal elements
“Given an integer array A of length n+2 with n>=2. It is known that at least two values stored in the array appear twice (i.e., there are at least two duplets). Implement and verify a program finding such two values. You may assume that the array contains values between 0 and n-1.“
Problem 1: Two-way sort
“We want to sort an array of Boolean values (assuming false < true) using only swaps.”
Problem 3: Ring Buffer
“We want to implement a queue data structure using a ring buffer.”