toward an automatic approach to greedy algorithms

The greedy approach is widely used for combinatorial optimization problems, but its implementation varies from problem to problem. In this paper we propose a mechanical approach for implementing greedy algorithmic programs. Using PAR, method, a problem can be continually partitioned into subproblems in smaller size based on the problem singleton and the maximum selector, and the greedy algorithm can be mechanically generated by combining the problem-solving sequences. Our structural model supports logical transformation from specifications to algorithmic programs by deductive inference; and thus significantly promotes the automation and reusability of algorithm design

a linear in-situ algorithm for the power of cyclic permutation

Natl. Univ. Defense Technology, School of Computer ScienceWe present and develop a linear in-situ algorithm for the power of a cyclic permutation Pr(-n< r < n). Several related algorithms become the special cases of this algorithm. At first, we used an abstract structure, named twin ring, to re

Automatic Algorithm Programming Model Based on the Improved Morgan's Refinement Calculus

The automatic algorithm programming model can increase the dependability and efficiency of algorithm program development, including specification generation, program refinement, and formal verification. However, the existing model has two flaws: incompleteness of program refinement and inadequate automation of formal verification. This paper proposes an automatic algorithm programming model based on the improved Morgan's refinement calculus. It extends the Morgan's refinement calculus rules and designs the C++ generation system for realizing the complete process of refinement. Meanwhile, the automation tools VCG (Verification Condition Generator) and Isabelle are used to improve the automation of formal verification. An example of a stock's maximum income demonstrates the effectiveness of the proposed model. Furthermore, the proposed model has some relevance for automatic software generation

Course Intelligent Brain Model Based on Crowd Intelligence

The development of artificial intelligence in education promotes the reform of teaching methods in the direction of intelligence and individuation. In this paper, the programming course is taken as an example to propose a curriculum intelligent brain model for open source swarm intelligence based on knowledge graph, and the bootstrapping framework is introduced to try to make the intelligent brain track the frontier like human beings and study several courses vertically. It studies the knowledge of subgraphs fusion of open-source software resources and domain semantics as well as the mining method of potential relationship, so that the intelligent brain can digest knowledge like human, and get through the course horizontally. Finally, knowledge discovery and natural representation based on knowledge graph enable intelligent brain to discover knowledge and solve problems just like human. This study provides new ideas, strategies, and application paths for the construction of knowledge graph based on big data and the integration of heterogeneous knowledge graph

A Unified Strategy for Formal Derivation and Proof of Binary Tree Nonrecursive Algorithms

In the formal derivation and proof of binary tree algorithms, Dijkstra's weakest predicate method is commonly used. However, the method has some drawbacks, including a time-consuming derivation process, complicated loop invariants, and the inability to generate executable programs from the specification. This paper proposes a unified strategy for the formal derivation and proof of binary tree non-recursive algorithms to address these issues. First, binary tree problem solving sequences are decomposed into two types of recursive relations based on queue and stack, and two corresponding loop invariant templates are constructed. Second, high-reliability Apla (abstract programming language) programs are derived using recursive relations and loop invariants. Finally, Apla programs are converted automatically into C++ executable programs. Two types of problems with binary tree queue and stack recursive relations are used as examples, and their formal derivation and proof are performed to validate the proposed strategy's effectiveness. This strategy improves the efficiency and correctness of binary tree algorithm derivation

A Method to Deduce and Synthesize the Dafny Programs

We propose a systematic method to deduce and synthesize the Dafny programs. First, the specification of problem is described in strict mathematical language. Then, the derivation process uses program specification transformation technology to perform equivalent transformation. Furthermore, Dafny program is synthesized through the obtained recursive relationship and loop invariants. Finally, the functional correctness of Dafny program is automatically verified by Dafny verifier or online tool. Through this method, we deduce and synthesize Dafny programs for many typical problems such as the cube sum problem, the minimum (or maximum) contiguous subarray problems, several searching problems, several sorting problems, and so on. Due to space limitation, we only illustrate the development process of Dafny programs for two typical problems: the minimum contiguous subarray problem and the new local bubble sorting problem. It proves that our method can effectively improve the correctness and reliability of Dafny program developed. What’s more, we demonstrate the potential of the deductive synthesis method by developing a new local bubble Sorting program

GPM-Based Multitemporal Weighted Precipitation Analysis Using GPM_IMERGDF Product and ASTER DEM in EDBF Algorithm

To obtain the high-resolution multitemporal precipitation using spatial downscaling technique on a precipitation dataset may provide a better representation of the spatial variability of precipitation to be used for different purposes. In this research, a new downscaling methodology such as the global precipitation mission (GPM)-based multitemporal weighted precipitation analysis (GMWPA) at 0.05° resolution is developed and applied in the humid region of Mainland China by employing the GPM dataset at 0.1° and the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) 30 m DEM-based geospatial predictors, i.e., elevation, longitude, and latitude in empirical distribution-based framework (EDBF) algorithm. The proposed methodology is a two-stepped process in which a scale-dependent regression analysis between each individual precipitation variable and the EDBF-based weighted precipitation with geospatial predictor(s), and to downscale the predicted multitemporal weighted precipitation at a refined scale is developed for the downscaling of GMWPA. While comparing results, it shows that the weighted precipitation outperformed all precipitation variables in terms of the coefficient of determination (R2) value, whereas they outperformed the annual precipitation variables and underperformed as compared to the seasonal and the monthly variables in terms of the calculated root mean square error (RMSE) value. Based on the achieved results, the weighted precipitation at the low-resolution (e.g., at 0.75° resolution) along-with the original resolution (e.g., at 0.1° resolution) is employed in the downscaling process to predict the average multitemporal precipitation, the annual total precipitation for the year 2001 and 2004, and the average annual precipitation (2001–2015) at 0.05° resolution, respectively. The downscaling approach resulting through proposed methodology captured the spatial patterns with greater accuracy at higher spatial resolution. This work showed that it is feasible to increase the spatial resolution of a precipitation variable(s) with greater accuracy on an annual basis or as an average from the multitemporal precipitation dataset using a geospatial predictor as the proxy of precipitation through the weighted precipitation in EDBF environment