### Table 5: Parameters and Training Time stricted to probabilistic context-free grammars. Af- ter completing the implementation of our move set, we plan to explore the modeling of context- sensitive phenomena. This work demonstrates that Solomono apos;s elegant framework deserves much fur- ther consideration.

1995

"... In PAGE 6: ...7% Table 3: Wall Street Journal-like arti cial grammar Inside-Outside algorithm in the rst two domains, while in the part-of-speech domain we are outper- formed by n-gram models but we vastly outperform the Inside-Outside algorithm. In Table5 , we display a sample of the number of parameters and execution time (on a Decstation 5000/33) associated with each algorithm. We choose n to yield approximately equivalent performance for each algorithm.... ..."

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### Table 18. ARWB Deterministic and Probabilistic Closure Results.

"... In PAGE 16: ... Approximately 8 iterations were necessary to obtain convergence, requiring approximately 2 hours of CPU time. Table18 contains a listing of the vehicle-level metrics for both the deterministic results and the probabilistic results. For the probabilistic analysis, the engine T/W at sea- level decreased from an optimistic 64.... ..."

### Table 2: Properties of static probabilistic combination strategies

"... In PAGE 12: ...roposition 2.12 Let C3BU AI C3BUBRB4CPBN CQB5 with two distinct basic events CP and CQ. Let AA, A8, and A9 be the static probabilistic combination strategies for C3BU. Then, the conditions shown in Table2 hold for all probabilistic pairs D4BD BP B4CTBDBN CJD0BDBN D9BDCLB5 and D4BE BP B4CTBEBN CJD0BEBN D9BECLB5 such that C3BU CJ CUB4CPBN CJD0BDBN D9BDCLB5BN B4CQBN CJD0BEBN D9BECLB5CV is satisfiable. That is, ignorance is always an envelope for a sound approximation of the combination of D4BD and D4BE.... ..."

### Table 2 Properties of static probabilistic combination strategies.

2001

"... In PAGE 12: ... Let a59 , a60 , and a61 be the static probabilistic combination strategies for a138a82a139 . Then, the conditions shown in Table2 hold for all probabilistic pairs a90 a52 a100 a20a62a19 a52 a14a37a12 a13 a52 a14a5a16 a52 a17a21a27 and a90 a57 a100a173a20a62a19 a57 a14a37a12 a13 a57 a14a5a16 a57 a17a21a27 such that a138a82a139a152a198 a102a137a20a77a185a22a14a37a12 a13a62a52a37a14a5a16a25a52a5a17a21a27a38a14a37a20a62a104a37a14a37a12 a13a148a57a121a14a5a16a64a57a2a17a21a27a26a107 is satisfiable. That is, ignorance is always an envelope for a sound approximation of the com- bination of a90a75a52 and a90a22a57 .... ..."

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### Table 1 summarizes the relations between the complexity classes, probabilistic satis ability prob- lems, belief network problems, and planning prob- lems discussed.

1999

"... In PAGE 4: ...satis ability problem Boolean formula belief network problem planning problem NP Sat 9x1; : : : ; 9xn(E[ (x)] ) most probable explanation best trajectory PP Majsat Rx1; : : : ; R xn(E[ (x)] ) belief updating (inference) plan evaluation NPPP E-Majsat 9x1; : : : ; 9xc; R xc+1; : : : ; R xn(E[ (x)] ) maximum a posteriori hypothesis best polynomial size plan PSPACE SSat 9x1; R x2; : : : ; 9xn?1; Rxn(E[ (x)] ) in uence diagrams best polynomial horizon plan Table1 : Di erent arrangements of quanti ers result in P-Sat problems complete for di erent complexity classes and correspond to basic problems in uncertain reasoning and planning. here, but the reduction essentially consists of creat- ing one variable per node in the belief network and one per conditional probability table entry.... ..."

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### Table 1: Websites that offered lesson plans with an approximate number of lesson plans offered and the URL of the web site

2006

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### Table 1. Research planning

"... In PAGE 5: ...halves, consisting of 6 months each. Table1 gives an approximate time schedule of the project. After each phase and/or subphase of the research project, based on the current achievements and results, technical reports, and conference, workshop and journal papers have been, are being and will be prepared and published.... ..."

### Table 6. Results of the evaluation second phase (probabilistic structure classes).

2006

"... In PAGE 13: ...able 6. Results of the evaluation second phase (probabilistic structure classes). to solve uniquely 2 and 3 instances, respectively, so none of the three strongest solvers is subsumed by the portfolio including all the solvers. In Table6 we report second phase results about random instances (2640 instances), divided into four categories: Model A 1200 instances, generated according to the guidelines presented in Section 3. Planning 120 instances, corresponding to the four Robot families in the suite Narizzano.... In PAGE 14: ...Table6 is arranged analogously to Table 5. Looking at Table 6, the first observation is that it is difficult to identify a group of solvers that performs well across different categories.... In PAGE 14: ...Looking at Table6 , the first observation is that it is difficult to identify a group of solvers that performs well across different categories. For instance, while ssolve turns out to be the best on three categories out of four, namely Model A, Planning, and QHorn, it is only third best on Nested Counterfactuals instances.... ..."

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### Table 6. Results of the evaluation second phase (probabilistic structure classes).

2006

"... In PAGE 14: ...In Table6 we report second phase results about random instances (2640 instances), divided into four categories: Model A 1200 instances, generated according to the guidelines presented in Section 3. Planning 120 instances, corresponding to the four Robot families in the suite Narizzano.... In PAGE 14: ... Nested Counterfactuals 1080 instances, generated according to the guidelines presented in Section 3. Table6 is arranged analogously to Table 5. Looking at Table 6, the rst observation is that it is di cult to identify a group of solvers that performs well across di erent categories.... In PAGE 14: ... Table 6 is arranged analogously to Table 5. Looking at Table6 , the rst observation is that it is di cult to identify a group of solvers that performs well across di erent categories. For instance, while ssolve turns out to be the best on three categories out of four, namely Model A, Planning, and QHorn, it is only third best on Nested Counterfactuals instances.... ..."

Cited by 3