### Table 1: The results from applying the bisimulation minimization algorithm to tree automata that arose in the verification of protocols Perculate and Leader.

"... In PAGE 14: ... The protocol is further described in [4]. Table1 shows the execution time, and the size of the tree automata before and after running our minimization algorithm.... ..."

### Table 1 shows the execution time, and the size of the tree automata before and after running our minimization algorithm.

2006

"... In PAGE 20: ... Table1 : The results from applying the bisimulation minimization algorithm to tree automata that arose in the verification of protocols Perculate and Leader. 7 Conclusion and future work We have extended an algorithm by Paige and Tarjan for solving the coarsest stable partition problem to the domain of trees, and obtained a running time of O( r m log n), where r is the maximum rank of the input alphabet, m is the total size of the transition table, and n is the number of states.... ..."

Cited by 5

### Table 4: The numerical (dnum) estimate of the refocusing resolution for time reversal through random media and comparison with the deterministic case.

2001

"... In PAGE 16: ... For the three other snapshots we a use random media with the same correlation length but with different variance for the fluctuations. The characteristics of the different random media are given in Table4 . We also give in this table the maximum contrast for each medium.... In PAGE 18: ... We calculate the refocusing resolution (dnum) as before by a least squares fit of the curvature at the peak amplitude (in the cross-range direction). The results are given in Table4 , where in the last column we compute the enhancement in the refocusing resolution in the random medium by comparing it to that obtained in the deterministic case. This is the super-resolution effect caused by multipathing.... In PAGE 18: ...Table 4: The numerical (dnum) estimate of the refocusing resolution for time reversal through random media and comparison with the deterministic case. The results shown in Table4 demonstrate quantitatively the super-resolution phenomenon: in media with random heterogeneities the refocusing resolution beats the diffraction limit, which is the refocusing resolution in the homogeneous medium. We see clearly that better resolution is obtained as the standard deviation of the fluctuations in the random media increases.... ..."

Cited by 5

### Table 2. Average number of states of Aho-Corasick, Spi and minimized automata for the case of two seeds

2007

"... In PAGE 10: ... This means that although the size of the union of individual seed automata could potentially grow as the product of sizes, it actually does not, as it is bounded by the size of the Aho-Corasick automaton which grows additively with respect to subsets of underlying words. In practice, our automaton is still substantially smaller than the Aho-Corasick automaton, as illustrated by Table2 . Similar to Table 1, 10000 random seed pairs have been... ..."

### Table 2. Average number of states of Aho-Corasick, Spi and minimized automata for the case of two seeds

2007

"... In PAGE 10: ... This means that although the size of the union of individual seed automata could potentially grow as the product of sizes, it actually does not, as it is bounded by the size of the Aho-Corasick automaton which grows additively with respect to subsets of underlying words. In practice, our automaton is still substantially smaller than the Aho-Corasick automaton, as illustrated by Table2 . Similar to Table 1, 10000 random seed pairs have been... ..."

### Table 3: Invertible non-deterministic #0Dowchart symbols with their direct and reverse

### Table 2. Implementability of asynchronous automata with multiple initial states

2004

"... In PAGE 2: ...ity problem has the same complexity as for synchronous products in the nondeterministic case, but can be solved in polynomial time in the deterministic case ( Table2 , col- umn 3). Maybe surprisingly, a simple trick allows us to extend this result to the implementability problem modulo bisimulation, again when the implementation is required to be deterministic (Table 2, column 4).... In PAGE 2: ...ity problem has the same complexity as for synchronous products in the nondeterministic case, but can be solved in polynomial time in the deterministic case (Table 2, col- umn 3). Maybe surprisingly, a simple trick allows us to extend this result to the implementability problem modulo bisimulation, again when the implementation is required to be deterministic ( Table2 , column 4). The paper is organized as follows.... ..."

### Table 2. Implementability of asynchronous automata with multiple initial states

2004

"... In PAGE 2: ...ity problem has the same complexity as for synchronous products in the nondeterministic case, but can be solved in polynomial time in the deterministic case ( Table2 , col- umn 3). Maybe surprisingly, a simple trick allows us to extend this result to the implementability problem modulo bisimulation, again when the implementation is required to be deterministic (Table 2, column 4).... In PAGE 2: ...ity problem has the same complexity as for synchronous products in the nondeterministic case, but can be solved in polynomial time in the deterministic case (Table 2, col- umn 3). Maybe surprisingly, a simple trick allows us to extend this result to the implementability problem modulo bisimulation, again when the implementation is required to be deterministic ( Table2 , column 4). The paper is organized as follows.... ..."

### Table 2. Implementability of asynchronous automata with multiple initial states

"... In PAGE 2: ...) In [Zie89], Zielonka characterized the transition systems that can be imple- mented as an asynchronous automata modulo language equivalence. Combin- ing this result with several others from the literature, we show that the imple- mentability problem has the same complexity as for synchronous products in the nondeterministic case, but can be solved in polynomial time in the deterministic case ( Table2 , column 3). Maybe surprisingly, a simple trick allows us to extend this result to the implementability problem modulo bisimulation, again when the implementation is required to be deterministic (Table 2, column 4).... In PAGE 2: ... Combin- ing this result with several others from the literature, we show that the imple- mentability problem has the same complexity as for synchronous products in the nondeterministic case, but can be solved in polynomial time in the deterministic case (Table 2, column 3). Maybe surprisingly, a simple trick allows us to extend this result to the implementability problem modulo bisimulation, again when the implementation is required to be deterministic ( Table2 , column 4). Partly motivated by the complexity results, in the last part of the paper we present new prototype implementations for asynchronous automata synthesis... ..."

### Table 2. Algorithm Framework for GA-DFALS Algorithm: Learning Deterministic Finite-state Automaton Based on Genetic Algorithm (A Basis)

2006

"... In PAGE 8: ...dure [7], and it is so called standard genetic algorithm 4. The core of our learning system (Deterministic Finite-state Automaton Learning System Based on Genetic Algorithm, GA-DFALS) is based on this framework (see Table2 ). The genetic operators we used are fitness proportionate selection operator, uniform crossover operator, and point mutation operator.... ..."