測試的目的在檢驗實作是否符合其規格；測試的流程，無論在測試個案的開發階段或是量產產品的測試階段均是非常耗時耗資的。如何有效的設計測試個案以達到減少測試所需時間及花費是本論文所欲探討的主題。在此論文中，我們將要針對幾個高效能測試個案設計的主題進行研究及討論，包括：測試時序（測試時序的自動安排方法）、縮減測試時間（移除多餘的測試個案的方法及串聯測試個案的方法）及簡化測試系統（可同步測試個案的產生方法）；一些由測試記憶體及通訊協定所衍生出來的問題。
測試記憶體的目的是要檢驗記憶體晶片的時序及功能是否正常。我們將從解決自動測試時序安排的問題開始著手，本文所提出的方法可以同時把測試的目標、測試的規格及測試機的限制列入考慮。然後把指定測試時序的問題轉換成線性規劃（linear programming）的模型，由現存的線性規劃解決器自動解決。

多餘的測試個案（Redundant test cases）是可以移除而不會減低錯誤的包含率（fault coverage）。藉由移除多餘的測試個案來達成縮減測試時間，可同時運用於測試個案的開發階段（有明確的錯誤模型）及量產產品測試的階段（錯誤模型不明確，但可以蒐集到測試的結果）。在測試個案的開發階段，可以藉由分析每個測試個案在錯誤模型中可以偵測到的錯誤。選擇一組具有完整的錯誤包含率以及測試時間最少的測試個案當成測試程式，將使得量產產品測試的實施時間最短。然而在進入量產產品的測試後，也可能會有多餘的測試個案發生，其原因是來自於理論上的錯誤模型與實際上發生的結果有偏差所致。本文的方法是去蒐集及分析未通過測試的晶片其未通過的項目，並由這些未通過的項目來進一步移除多餘的測試個案。本文的研究結果顯示，這兩個移除多餘測試個案的問題是一樣的，都可以轉換成一個具權值的集合包含問題（weighted set-covering problem）。在實際應用上，我們可以將其轉換成整數型線性規劃（integer linear programming）的模型，由現存的線性規劃解決器自動解決。

在量產產品測試的過程中，我們可以利用串聯測試個案的方式，再進一步的縮減測試的時間。其主要的觀念是要充分的利用前一組測試個案所遺留下來的記憶體狀態，使得下一組測試個案可以省去設定初值的動作；而下一組測試個案的起始驗證動作也可以省去前一組測試個案的後段驗證動作。此外，測試機的信號設定時間也將因串聯的結果而減為最少。在本論文中，我們把串聯測試個案的問題轉換成一個鄉村中國郵差問題（rural Chinese postman problem），並加以解決。但是當我們把鄉村中國郵差問題轉換成一個整數型線性規劃的模型時，卻發現限制（constrains）的數目可能達到指數級（exponential），而無法直接列在一個模型上來解決。在本論文中，我們將提出限制漸增法來解決這個問題；而其方法主要是迴避直接列在一個模型所衍生的問題，轉而去解決一連串限制較少的整數型線性規劃模型，並分析解決鄉村中國郵差問題所需要的模型及限制數目。

測試的同步問題常發生在需要兩個以上的測試機來同步完成測試的測試系統中，因此常見於多方通訊協定（multi-party communication protocol）的測試。在本論文中，我們提出一個多重圖（multiplex digraph）模型來作為產生可同步測試個案的參考；多重圖模型可以適用於各種形式的測試系統架構，並可同時將測試個案所選用的輸出/輸入指令及同步指令的花費列入考慮；並將利用多重圖模型來產生花費最少的可同步的轉移序列、可同步的 T 方法序列、以及可同步的重疊 U 方法序列，並分析其複雜度。

The objective of testing is to see if an implementation conforms to its specification. Testing is costly and time-consuming on both development and test application phases. How to efficiently design test cases for minimizing test time and cost is considered. In this dissertation, we study several efficient test case problems, including timing issue (test timing assignment), test time reduction issues (redundant test cases removal and test cases interconnection), and test architecture simplification issue (synchronizable test case generation), which are arisen from memory testing and communication protocol testing.
The purpose of memory testing is to ensure that memory chip can work correctly in timing as well as functionality. We begin with solving timing assignment problem automatically. The proposed method is comprehensive enough to take the test objective and constraints from specification and tester into consideration. The test timing assignment problem is then transformed into a linear programming model, which can be automatically solved.

Redundant test cases can be removed without reducing fault coverage. Test time reduction by removing redundant test cases for both test development phase, which has a well-defined fault model, and production test phase, which has no fault model, is discussed. During the test development phase, the process is to analyze fault detectability with respect to a given fault model. An optimal set of test cases is selected to compose the final test program, which results in minimum test application time. After proceeding to the production test phase, redundancy can also exhibit due to dependency of faults or discord between theoretical and practical fault models. The process is to analyze fail labels to remove redundant test cases optimally. Our result shows that these two methods are just dual to each other, and moreover, their underlying problem is an instance of weighted set-covering problem. In practical application, these two problems can be transformed into integer linear programming models, which can be automatically solved.

As the production test process goes, a further test time reduction technique can be applied. The idea is to interconnect test cases to reuse memory states left from the previous test case for saving initialization and verification sequences as well as signal settling time of tester. The interconnection problem is transformed into an instance of Rural Chinese Postman (RCP) problem. However, the number of constraints could be exponential in the worst case if transforming RCP problem into an integer linear programming model. In this dissertation, a novel incremental constraining method is proposed, and our approach is to solve a number of successive integer linear programming models with smaller number of constraints. The total numbers of iterations and constraints applied to solve RCP problem are analyzed and compared.

The test synchronization problem happens in a special test architecture, which requires at least two remote testers to test the implementation coordinately. This problem is usually encountered in testing multi-party communication protocol implementations. Testing system can be significantly simplified if synchronizable test cases are applied. In this dissertation, we propose a multiplex digraph model for synchronizable test case generation, which will consider both the costs of input/output operations and external synchronization operations. Applications for generating minimum-cost synchronizable transfer sequence, T-method test sequence, and Overlapping U-method test sequence are discussed and analyzed.

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