### Table 5. Results on Boolean Circuit Induction Problems: comparison between NOVEL apos;s results on Sun SS 10/51 and GSAT apos;s published results [75] on SGI Challenge and Kamath et al. apos;s published results on VAX 11/780 [49].

1997

Cited by 18

### Table 6. Results on Boolean Circuit Induction Problems: comparison between NOVEL apos;s results on Sun SS 10/51 and Kamath et al. apos;s published results on VAX 11/780 [49] Problem NOVEL (Max-Flips= (5*#vars) per try) Kamath

1997

Cited by 18

### Table 3: The standard axioms of CRL for booleans, where b : Bool sidered di erent. According to axiom Bool2 there are at most two booleans. This axiom formally expresses the no-junk property of any model with respect to the booleans. (Axiom Bool2 is not nec- essary for proving properties of data; we only include it for completeness.) It is not hard to see that both the axioms Bool1 and Bool2 are sound in the valid models for the above speci cation. For the booleans, a basic form of induction can be derived: a property formula (b), where b : Bool, is proved if (t) and (f). De nition 3.1 (Case Distinction). The following inference rule is referred to as case distinction on b : Bool:

1994

Cited by 3

### Table 1: Inductive rules for EMPAvp integrated interleaving semantics 5

"... In PAGE 6: ... We denote by PMovevp = Act00 vp BExp Sub Gvp the set of all the potential moves, where Act00 vp = AType0 vp ARatevp with AType0 vp = ATypevp [ ANameIO. The formal de nition is based on the transition relation ???!, which is the least subset of Gvp (Act00 vp BExp Sub) Gvp satisfying the inference rule reported in the rst part of Table1 . This rule selects the potential moves having the highest priority level, and then merges together those having the same action type, the same priority level, the same boolean guard, the same assignment, and the same derivative term.... In PAGE 6: ... The second operation is carried out through function Meltvp : Mu n(PMovevp) ?! P n(PMovevp) and partial function Min : (ARatevp ARatevp) ?! o ARatevp, which are de ned in the fourth part of Table 1. The multiset PM vp(E) 2 Mu n(PMovevp) of potential moves of E 2 Gvp is de ned by structural induction in the second part of Table1 . The normalization of rates of potential moves resulting from the synchronization of an active action with several independent or alternative passive actions of the same name is carried out through partial function Normvp : (AType0 vp AType0 vp ARatevp ARatevp Mu n(PMovevp) Mu n(PMovevp)) ?!o ARatevp and function Split : (ARatevp R I ]0;1]) ?! ARatevp, which are de ned in the fth part of Table 1.... In PAGE 6: ...ultiset obtained by projecting the tuples in multiset M on their i-th component. Thus, e.g., ( 1(PM2))( lt; ; gt;) in the fth part of Table1 denotes the multiplicity of tuples of PM2 whose rst component is lt; ; gt;.... ..."

Cited by 1

### Tables 4, 5 and 6 lists the typical CRL axioms and rules for interaction between data and processes. The axioms for summation are denoted by SUM, the axioms for the conditional by COND and the rules for the booleans by BOOL. Beside the axioms and rules mentioned above, CRL incorporates two other important proof prin- ciples. First, it supports an principle for induction not only on data but also on data in processes. The second principle is RSP (Recursive Speci cation Principle) taken from [BW90] extended to processes with data. Informally, it says that each guarded recursive speci cation has at most one solution.

1994

Cited by 14

### Table 2: Effect of Induction-based Learning on BMC

"... In PAGE 5: ...1. Table2 shows the runtime for a few industrial instances. We can see that the induction-based learning can be very powerful, espe- cially for hard UNSAT cases.... ..."

### Table 2: Effect of Induction-based Learning on BMC

"... In PAGE 5: ...1. Table2 shows the runtime for a few industrial instances. We can see that the induction-based learning can be very powerful, espe- cially for hard UNSAT cases.... ..."

### Table 2.2: Effect of Induction-based Learning on BMC

2005

### lable: boolean);

in Simple and Integrated Heuristic Algorithms for Scheduling Tasks with Time and Resource Constraints

1987

Cited by 21

### Table 2: E ect of Classi cation Noise: Random Boolean Functions of error rates studied, the di erence in gross accuracies consistently shows an advantage of at least one percentage point for the naive strategy. Thus, in a sense, over the space of possible true models, it is C = A1 and C = A1 _(A2 ^A3) that are anomalous. Most boolean relations are like parity in that, when they underlie data generation as described, it is best to ignore over tting in inducing decision trees. This does not mean, of course, that the same is true of problems on which researchers have generally tested decision tree induction methods. Rather, the fact that published methods have often proven e ective lends weight to the conclusion that the problems to which decision tree methods have been applied are a small and very special subclass. 4.5 The E ect of Over tting Avoidance is Representation Dependent

"... In PAGE 27: ... In each trial, a relation between C and A1 through A5 is chosen at random over the space of all 225 boolean functions of ve variables. Table2 shows a pattern of results much in line with those presented for the parity problem in Table 1. As error rates increase, the naive and sophis- ticated strategies disagree more often; and at every level of noise the naive strategy proves superior.... ..."