A Reduction-Preserving Completion for Proving Confluence of Non-Terminating Term Rewriting Systems

We give a method to prove confluence of term rewriting systems that contain non-terminating rewrite rules such as commutativity and associativity. Usually, confluence of term rewriting systems containing such rules is proved by treating them as equational term rewriting systems and considering E-critical pairs and/or termination modulo E. In contrast, our method is based solely on usual critical pairs and it also (partially) works even if the system is not terminating modulo E. We first present confluence criteria for term rewriting systems whose rewrite rules can be partitioned into a terminating part and a possibly non-terminating part. We then give a reduction-preserving completion procedure so that the applicability of the criteria is enhanced. In contrast to the well-known Knuth-Bendix completion procedure which preserves the equivalence relation of the system, our completion procedure preserves the reduction relation of the system, by which confluence of the original system is inferred from that of the completed system

Formalising Confluence in PVS

Confluence is a critical property of computational systems which is related with determinism and non ambiguity and thus with other relevant computational attributes of functional specifications and rewriting system as termination and completion. Several criteria have been explored that guarantee confluence and their formalisations provide further interesting information. This work discusses topics and presents personal positions and views related with the formalisation of confluence properties in the Prototype Verification System PVS developed at our research group.Comment: In Proceedings DCM 2015, arXiv:1603.0053

Abstract Canonical Inference

An abstract framework of canonical inference is used to explore how different proof orderings induce different variants of saturation and completeness. Notions like completion, paramodulation, saturation, redundancy elimination, and rewrite-system reduction are connected to proof orderings. Fairness of deductive mechanisms is defined in terms of proof orderings, distinguishing between (ordinary) "fairness," which yields completeness, and "uniform fairness," which yields saturation.Comment: 28 pages, no figures, to appear in ACM Trans. on Computational Logi

Single-machine scheduling with stepwise tardiness costs and release times

We study a scheduling problem that belongs to the yard operations component of the railroad planning problems, namely the hump sequencing problem. The scheduling problem is characterized as a single-machine problem with stepwise tardiness cost objectives. This is a new scheduling criterion which is also relevant in the context of traditional machine scheduling problems. We produce complexity results that characterize some cases of the problem as pseudo-polynomially solvable. For the difficult-to-solve cases of the problem, we develop mathematical programming formulations, and propose heuristic algorithms. We test the formulations and heuristic algorithms on randomly generated single-machine scheduling problems and real-life datasets for the hump sequencing problem. Our experiments show promising results for both sets of problems

Meja kopi modular untuk rumah minimalis moden

Peningkatan populasi di seluruh dunia adalah sangat tinggi. Di Malaysia, kadar pertumbuhan populasi rakyat Malaysia meningkat kepada 1.1% iaitu sebanyak 32.4 bilion (2018) berbanding 31.1 bilion (2015) (Mahidin, 2019). Peningkatan populasi ini meningkatkan permintaan dan bekalan terhadap keperluan asasi seperti makanan, pakaian, peluang pekerjaan dan juga ruang kediaman. Ini turut mempengaruhi reka bentuk dan saiz kediaman bagi menempatkan kesemua rakyat Malaysia dan juga pekerja asing yang berkerja di negara ini. Menurut Harian Metro Online, tanah yang semakin berkurangan menyebabkan unit kediaman sekarang banyak dibina dengan keluasan yang terhad antara 650 hingga 800 kaki persegi (Satibi, 2018). Justeru, pemilihan perabot memainkan peranan penting dalam usaha untuk menampakkan kediaman lebih luas dan selesa (Ismail, 2020)