1. What contributions have the authors mentioned in the paper "Structural counter abstraction" ?
The authors present the first method to automatically prove fair termination of depth-bounded systems.. What makes their approach unique is the way in which it exploits the well-structuredness of the analyzed system.. The authors have implemented their work in a prototype tool and used it to automatically prove liveness properties of complex concurrent systems, including nonblocking algorithms such as Treiber ’ s stack and several distributed processes.
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2. How do the authors eliminate the intermediate steps?
The authors eliminate the intermediate steps by using the quantifier elimination procedure for linear integer arithmetic in PRINCESS [23].
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3. How many variables did the authors get from the inductive invariant?
For instance, for Treiber’s stack, having one variable for each vertex of each nested graph in the inductive invariant and those obtained by applying rewrite rules led to an abstraction with over 170 variables and 40 transitions.
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4. What is the labeling function for a graph?
The authors define (vertex) labeled graphs over a set of labels VL as graphs with labels for each vertex and denote them as (V,E, ν) where ν : V → VL is the vertex-labeling function.
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![Fig. 1. Source code of Treiber’s stack [24] on the left and its abstraction as a depth-bounded graph transformation system on the right.](/figures/fig-1-source-code-of-treibers-stack-24-on-the-left-and-its-109rbk7l.webp)
