### Table 1: The progression algorithm.

1998

"... In PAGE 9: ... The technique of formula progression works by labeling the initial state with the sentence representing the goal, call it g.For each successor of the initial state, generated byforward chaining, a new formula label is generated by progressing the initial state apos;s label using the algorithm given in Table1 . This new formula is used to label the successor states.... ..."

Cited by 109

### Table 1: The progression algorithm.

1995

"... In PAGE 5: ...5 We have developed a mechanism for doing incremental checking of an LTL formula. The key to this method is the progression algorithm given in Table1 . In the algorithm quantified formulas are progressed by progressing all of their instances.... In PAGE 8: ... Our planner can take this first-order definition of a predicate (rewritten in Lisp syntax) as input. And we can then use this predicate in an LTL control formula where during the oper- ation of the progression algorithm ( Table1 ) its first-order definition will be evaluated in the current world for various instantiations of its parameter x. Hence, we can use a strategy of preserving good towers by setting our LTL control formula to 2 8[x:clear(x)] goodtower(x) ) goodtowerabove(x) ; (1) where the predicate goodtowerabove is defined in a manner that is symmetric to goodtowerbelow.... ..."

Cited by 77

### Table 1: The progression algorithm.

1995

"... In PAGE 6: ... We have developed a mecha- nism for doing incremental checking of an LTL formula. The key to this method is the progression algorithm given in Table1 . In the algorithm quantified formulas are progressed by progressing all of their instances.... In PAGE 9: ... Our planner can take this first-order definition of a predicate (rewritten in Lisp syntax) as input. And we can then use this predicate in an LTL control formula where during the operation of the progression algorithm ( Table1 ) its first-order definition will be evaluated in the current world for various instantiations of its parameter x. Hence, we can use a strategy of preserving good towers by setting our LTL control formula to 2 8[x:clear(x)] goodtower(x) ) goodtowerabove(x) ; (1) where the predicate goodtowerabove is defined in a manner that is symmetric to goodtowerbelow.... ..."

Cited by 77

### Table 1: The progression algorithm.

1995

"... In PAGE 5: ...5 We have developed a mechanism for doing incremental checking of an LTL formula. The key to this method is the progression algorithm given in Table1 . In the algorithm quantified formulas are progressed by progressing all of their instances.... In PAGE 8: ... Our planner can take this first-order definition of a predicate (rewritten in Lisp syntax) as input. And we can then use this predicate in an LTL control formula where during the oper- ation of the progression algorithm ( Table1 ) its first-order definition will be evaluated in the current world for various instantiations of its parameter x. Hence, we can use a strategy of preserving good towers by setting our LTL control formula to 2 8[x:clear(x)] goodtower(x) ) goodtowerabove(x) ;; (1) where the predicate goodtowerabove is defined in a manner that is symmetric to goodtowerbelow.... ..."

Cited by 77

### Table 3. Comparison of formal methods used for swarm specifications. Name COW Algorithm Tool Formal Emergent Used in

"... In PAGE 4: ... It was also found that in recent years there have been a large number of hybrid or combination formal methods that have been developed with the hope of specifying both concurrency and algorithms with the same method. Table 1 shows part of the results of the survey for mainstream formal methods, Table 2 shows the results for hybrid formal methods and Table3 shows a comparison of formal methods that have been used to specify swarm-based systems. Table 1 summarizes the results of mainstream formal techniques and their use on swarm and agent-based systems.... In PAGE 6: ... Statecharts Temporal Yes Yes No Yes Yes No B Temporal Yes No No Yes Yes No Petri Nets Timed Yes Yes No Yes Yes No comm. Object Z Timed Yes No Yes Yes Yes No CSP zccs Yes Yes No Yes Yes No Table3 compares methods that have been used for modeling or specifling swarm-based systems (computer or biological based). It lists whether each method provides support for concurrency, algorithms, has tool support, is based on a formal foundation, and if it supports the analysis of emergent behavior and whether it has been used to specify swarm-based systems (software or biological).... ..."

### Table 1. Steps Showing Progress of Access Analysis

"... In PAGE 5: ... The code contains two read accesses (1 and 3) and three write accesses (2, 4 and 5). Table1 shows the progress of access analysis whilst traversing the CFG. The final access triple for this clock cycle is ( [ ], [ {2, 5} ], [ {3, 4, 1} ] ), which can be assigned to a memory with one write port and... ..."

### Table 1: Quantitative analysis of the detection/tracking modules

1998

"... In PAGE 4: ... This scalar value allows us to discard detected blobs which are due to misregistrationof the motioncompen- sation algorithm, since these regions have no temporal coherence which is characterized by a small length. Table1 gives some results obtained over several set of video streams acquired by the Predator UAV and VSAM platforms. These video streams represent a va- riety of scenes involving human activity (see figures 1 and 3), and were used to evaluate the performance of our system.... ..."

Cited by 6

### Table 1: Simulation track parameters.

"... In PAGE 6: ... The map covers a part of central Sweden and is stored in a uniform grid of 50 m spacing. The algorithms are evaluated in Monte Carlo simula- tions, the aircraft tracks were generated using Gaus- sian distributed initial aircraft position and zero mean Gaussian noises fvtg and fetg, the parameters are listed in Table1 . The simulation tracks are displayed... ..."

### Table 3: Mean length of reconstructed tracks, resolutions and pulls for primary tracks.

"... In PAGE 16: ... Ideally, the distributions of pulls should be unbiased and have a Gaussian core of unity. Table3 presents values of pulls and residuals for four parameters x, y, tx and ty of properly reconstructed tracks and the mean length of the tracks given in the number of associated hits for all three algorithms. As can be seen, pulls for the reconstructed tracks are typically wider than unity.... In PAGE 18: ...Table3 ) on hb-mu2 computer (Pentium III), the mean CPU time needed for CATS to reconstruct one mixed event was about 240 ms. A comparison of the computing time dependence on the number of superimposed inelastic events for CATS and RANGER is shown in Fig.... ..."

### Table 4. Progress of SEQFIT algorithm in Example 3

in CONTENTS

1963

"... In PAGE 16: ...532 0.540 The progress of the computation is summarized in Table4 , and the final breakpoints and coefficients are given in Table 5. This approximator is not proposed as a useful approximator for sine, but was computed for the purpose of observing the behavior of SEQFIT in approxi- mating an oscillating function.... ..."