Minimizing the Number of States in Incompletely Specified Sequential Switching Functions

Paull, Marvin C.; Unger, Stephen H.

doi:10.1109/tec.1959.5222697

Cited by 277 publications

(73 citation statements)

References 5 publications

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“…By considering a collection of n/3 independent triangles, we see that this bound is best possible. Paull & Unger [36] designed a procedure that generates all maximal independent sets in a graph in O(n 2 ) time per generated set. Based on the ideas introduced by Lawler [26], we present a dynamic program across the subsets with a time complexity of O * (2.4422 n ).…”

Section: The Travelling Salesman Problem (Tsp)mentioning

confidence: 99%

Exact Algorithms for NP-Hard Problems: A Survey

Woeginger

2003

Lecture Notes in Computer Science

495

271

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Abstract. We discuss fast exponential time solutions for NP-complete problems. We survey known results and approaches, we provide pointers to the literature, and we discuss several open problems in this area. The list of discussed NP-complete problems includes the travelling salesman problem, scheduling under precedence constraints, satisfiability, knapsack, graph coloring, independent sets in graphs, bandwidth of a graph, and many more.

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Section: The Travelling Salesman Problem (Tsp)mentioning

confidence: 99%

Exact Algorithms for NP-Hard Problems: A Survey

Woeginger

2003

Lecture Notes in Computer Science

495

271

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“…An efficient algorithm for computing such compatible and incompatible state-pairs is based on the use of merger tables (Kohavi, 1978;Paull, and Unger, 1959 Heymann & Degani, 2007 for the details of the algorithmic procedure for generating compatibles). The next step consists of collecting from the maximal compatibles a suitable subset adequate for construction of a correct and succinct user model.…”

Section: Generation Of User Models and Interfacesmentioning

confidence: 99%

Modeling and Formal Analysis of Human-Machine Interaction

Heymann

Degani²,

Shafto

2013

Oxford Handbooks Online

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We describe a formal, model-based, approach for the analysis and design of human-automation interaction. The approach is guided by two primary objectives: first, that the interaction be correct in the sense that it will enable the user to operate the system reliably; second, that the interaction be as simple as possible while maintaining all the required operational flexibility. With these objectives we first discuss a methodology for verification of user-interface correctness, thereby addressing the issue of operational reliability, and then present an algorithmic approach for designing simple and succinct interfaces.

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“…We reduce the problem to the minimization problem of incompletely specified finite state machines [15]. The L Sep algorithm translates the 3DFA C i into an incompletely specified finite state machine M. It then invokes the algorithm in [15] to obtain a minimal finite state machine M i consistent with M. Finally, M i is converted to a DFA A i .…”

Section: Finding a Minimal Consistent Dfamentioning

confidence: 99%

“…We first use Paull and Unger's algorithm [15] to find the sets of "maximal" compatible states 6 , which are the candidates for the states in the reduced DFA. Consider an example shown in Figure 5.…”

Section: Heuristics For Efficiencymentioning

confidence: 99%

Learning Minimal Separating DFA’s for Compositional Verification

Chen

Farzan

Clarke

et al. 2009

Tools and Algorithms for the Construction and Analysis of Systems

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Abstract. Algorithms for learning a minimal separating DFA of two disjoint regular languages have been proposed and adapted for different applications. One of the most important applications is learning minimal contextual assumptions in automated compositional verification. We propose in this paper an efficient learning algorithm, called L Sep , that learns and generates a minimal separating DFA. Our algorithm has a quadratic query complexity in the product of sizes of the minimal DFA's for the two input languages. In contrast, the most recent algorithm of Gupta et al. has an exponential query complexity in the sizes of the two DFA's. Moreover, experimental results show that our learning algorithm significantly outperforms all existing algorithms on randomly-generated example problems. We describe how our algorithm can be adapted for automated compositional verification. The adapted version is evaluated on the LTSA benchmarks and compared with other automated compositional verification approaches. The result shows that our algorithm surpasses others in 30 of 49 benchmark problems.

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Minimizing the Number of States in Incompletely Specified Sequential Switching Functions

Cited by 277 publications

References 5 publications

Exact Algorithms for NP-Hard Problems: A Survey

Exact Algorithms for NP-Hard Problems: A Survey

Modeling and Formal Analysis of Human-Machine Interaction

Learning Minimal Separating DFA’s for Compositional Verification

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