The boundary conditions (BCs) have shown great potential in requirements engineering because a BC captures the particular combination of circumstances, i.e., divergence, in which the goals of the requirement cannot be satisfied as a whole. Existing researches have attempted to automatically identify lots of BCs. Unfortunately, a large number of identified BCs make assessing and resolving divergences expensive. Existing methods adopt a coarse-grained metric, generality, to filter out less general BCs. However, the results still retain a large number of redundant BCs since a general BC potentially captures redundant circumstances that do not lead to a divergence. Furthermore, the likelihood of BC can be misled by redundant BCs resulting in costly repeatedly assessing and resolving divergences. In this paper, we present a fine-grained metric to filter out the redundant BCs. We first introduce the concept of contrasty of BC. Intuitively, if two BCs are contrastive, they capture different divergences. We argue that a set of contrastive BCs should be recommended to engineers, rather than a set of general BCs that potentially only indicates the same divergence. Then we design a post-processing framework (PPFc) to produce a set of contrastive BCs after identifying BCs. Experimental results show that the contrasty metric dramatically reduces the number of BCs recommended to engineers. Results also demonstrate that lots of BCs identified by the state-of-the-art method are redundant in most cases. Besides, to improve efficiency, we propose a joint framework (JFc) to interleave assessing based on the contrasty metric with identifying BCs. The primary intuition behind JFc is that it considers the search bias toward contrastive BCs during identifying BCs, thereby pruning the BCs capturing the same divergence. Experiments confirm the improvements of JFc in identifying contrastive BCs.

An answer set program with variables is first-order definable on finite structures if the set of its finite answer sets can be captured by a first-order sentence, otherwise this program is first-order indefinable on finite structures. In this paper, we study the problem of first-order indefinability of answer set programs. We provide an Ehrenfeucht-Fraisse game-theoretic characterization for the first-order indefinability of answer set programs on finite structures. As an application of this approach, we show that the well-known finding Hamiltonian cycles program is not first-order definable on finite structures. We then define two notions named the 0-1 property and unbounded cycles or paths under the answer set semantics, from which we develop two sufficient conditions that may be effectively used in proving a program's first-order indefinability on finite structures under certain circumstances.

In this paper we apply computer-aided theorem discovery technique to discover theorems about strongly equivalent logic programs under the answer set semantics. Our discovered theorems capture new classes of strongly equivalent logic programs that can lead to new program simplification rules that preserve strong equivalence. Specifically, with the help of computers, we discovered exact conditions that capture the strong equivalence between a rule and the empty set, between two rules, between two rules and one of the two rules, between two rules and another rule, and between three rules and two of the three rules.