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On the learnability of Boolean formulae
1987
Proceedings of the nineteenth annual ACM conference on Theory of computing - STOC '87
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Acknowledgements We w ould like to thank Umesh Vazirani for many helpful ideas and discussions on learning under uniform distributions. ...
In section 3 w e discuss closure under boolean operations on the members of the learnable classes. ...
Since learnability m a y depend on the representation chosen, we de ne learnability of a class of representations of boolean concepts, as opposed to de ning learnability of the concepts themselves. ...
doi:10.1145/28395.28426
dblp:conf/stoc/KearnsLPV87
fatcat:q7pi5rwh2vhcvmmljaklerwcay
Understanding Boolean Function Learnability on Deep Neural Networks
[article]
2021
arXiv
pre-print
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Computational learning theory states that many classes of boolean formulas are learnable in polynomial time. ...
Specifically, we analyse boolean formulas associated with the decision version of combinatorial optimisation problems, model sampling benchmarks, and random 3-CNFs with varying degrees of constrainedness ...
Moshe Vardi is supported in part by NSF grants IIS-1527668, CCF-1704883, IIS-1830549, DoD MURI grant N00014-20-1-2787, and an award from the Maryland Procurement Office. ...
arXiv:2009.05908v2
fatcat:ry2evqrirnefzizzhppafjtx5m
Can complexity theory benefit from Learning Theory?
[chapter]
1993
Lecture Notes in Computer Science
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Using known results on efficient query-learnability of some Boolean concept classes, we prove several (co-NP-completeness) results on the complexity of certain decision problems concerning representability ...
of general Boolean functions in special forms. ...
One can show that f ~ 1 if and only if g can be expressed as a read-once DNF. The case of read-twice DNF formulas is handled analogously. ...
doi:10.1007/3-540-56602-3_150
fatcat:6owkpchugbcvbcnv4rviw2u2fy
Almost all monotone Boolean functions are polynomially learnable using membership queries
2001
Information Processing Letters
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It is shown that almost all monotone Boolean functions are polynomially identifiable in the input number of variables as well as the output being the sum of the sizes of the CNF and DNF representations ...
We consider exact learning or identification of monotone Boolean functions by only using membership queries. ...
In the context of Boolean formulae, the algorithm queries an oracle for the value of the formula f on a particular variable assignment a. ...
doi:10.1016/s0020-0190(00)00225-8
fatcat:lluk3uo3h5cx5a44oiekxsk6zm
Exact Learning Boolean Functions via the Monotone Theory
1995
Information and Computation
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We study the learnability of boolean functions from membership and equivalence queries. ...
We develop the Monotone Theory that proves 1 Any boolean function is learnable in polynomial time in its minimal DNF size, its minimal CNF size and the number of variables n. ...
On the other hand, many other results gave subclasses of boolean functions that are learnable in their DNF representations. ...
doi:10.1006/inco.1995.1164
fatcat:bjug3shh2ffbtnyzcwaxvbhi4m
A Dichotomy Theorem for Learning Quantified Boolean Formulas
1999
Machine Learning
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We consider the following classes of quantified boolean formulas. Fix a finite set of basic boolean functions. ...
We prove the following dichotomy theorem: For any set of basic boolean functions, the resulting set of formulas is either polynomially learnable from equivalence queries alone or else it is not PAC-predictable ...
Later on, we will use this property to show the learnability of quantified boolean formulas constructed using these families of basis. Let us state the main result of this section: Lemma 7. ...
doi:10.1023/a:1007582729656
dblp:journals/ml/Dalmau99
fatcat:c36p2kzlgbc7xg2cc47izw7q6e
Learning decision lists
1987
Machine Learning
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normal form with at most k literals per term), and decision trees of depth k, our result strictly increases the set of functions that are known to be polynomially learnable, in the sense of Valiant (1984 ...
Since k-DL properly includes other well-known techniques for representing Boolean functions such as h-CNF (formulae in conjunctive normal form with at most k literals per clause), k-DNF (formulae in disjunctive ...
the referees for their very helpful comments on an earlier version of this paper. ...
doi:10.1007/bf00058680
fatcat:7m4sbslcm5bsflben4w6regl6m
On the learnability of Zn-DNF formulas (extended abstract)
1995
Proceedings of the eighth annual conference on Computational learning theory - COLT '95
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Although many learning problems can be reduced to learning Boolean functions, in many ...
This shows that the difficult y of learning Boolean DNF formulas lies in the fact that the domain is small. ...
In Blum
and Singh
[BS90]
it was proved
that
for any constant
k, Boolean
functions
of k monomials
are pat-learnable
by the more expressive
hypothesis
class of general
DNF
formulas. ...
doi:10.1145/225298.225322
dblp:conf/colt/BshoutyCDH95
fatcat:hyakjt5uanhtfdoutcko5gqleu
Computational learning theory
1992
Proceedings of the twenty-fourth annual ACM symposium on Theory of computing - STOC '92
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Learning in the presence of malicious errors. In Proceedings of the Twentieth Annual ACM Symposium on Theory of Computing, pages 267-280. ACM Press, 1988. learnability of boolean formulae. ...
6.1
Classes of boolean
formulas
Valiant [131] shows monomials
and k-CNF formulas are
properly
PAC-learnable
using only positive examples. ...
doi:10.1145/129712.129746
dblp:conf/stoc/Angluin92
fatcat:7aw3cnd745bellyhu7phywpul4
Learning from recursive, tree structured examples
[chapter]
1994
Lecture Notes in Computer Science
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We show that in the PAC framework def'med by Valiant [10], the extensions to this model of two Boolean formula classes: k-DNF and k-DL, remain polynomially learnable. ...
A signature enables us to define the set of all a/lowed (partial or complete) representations. This model properly contains Boolean representations. ...
This is why we focus on PAC learning and show (in Section 3) that the natural extensions of two of the main Boolean formula classes, k-DNF and k-DL, stay polynomially learnable. ...
doi:10.1007/3-540-57868-4_75
fatcat:o67oadxwxzhlnkt2etsddda6iq
Exact Learning when Irrelevant Variables Abound
[chapter]
1999
Lecture Notes in Computer Science
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Any Boolean function of O(logn) relevant variables can be exactly learned with a set of non-adaptive membership queries alone and a minimum sized decision tree representation of the function constructed ...
We show that truth-table minimization of decision trees can be done in polynomial time, complementing the well-known result of Masek that truth-table minimization of DNF formulas is NP-hard. ...
Domingo for communicating the problem of exact learning Boolean functions of few relevant variables with membership queries. We also thank L. ...
doi:10.1007/3-540-49097-3_8
fatcat:cuf62jnrsfhdpcj4gnj4o45ona
Nonuniform learnability
1994
Journal of computer and system sciences (Print)
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Some examples (Boolean formulae, recursive, and r.e. sets) are shown to be nonuniformly learnable by a polynomial (in the size of the representation of the concept and in the error parameters) number of ...
The learning model of Valiant is extended to allow the number of examples required for learning to depend on the particular concept to be learned, instead of requiring a uniform bound for all concepts ...
., "is the set of Boolean formulae polynomially learnable?" We show that Boolean formulae are learnable by polynomially many examples. However, the learning time of our algorithm is not polynomial. ...
doi:10.1016/s0022-0000(05)80005-4
fatcat:4xlsvlxn25fvrbgd74x3u2xen4
A dichotomy theorem for learning quantified Boolean formulas
1997
Proceedings of the tenth annual conference on Computational learning theory - COLT '97
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We consider the following classes of quanti ed boolean formulas. Fix a nite set of basic boolean functions. ...
We prove the following dichotomy theorem: For any set of basic boolean functions, the resulting set of formulas is either polynomially learnable from equivalence queries alone or else it is not PAC-predictable ...
If S satis es one of the conditions (a)-(d) below, then C 98-Formula(S) is polynomially exactly learnable with improper equivalence queries. ...
doi:10.1145/267460.267496
dblp:conf/colt/Dalmau97
fatcat:nakyr3lzbzaebdame7nfuijd5q
A necessary condition for learning from positive examples
1990
Machine Learning
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The criterion is applied to several types of Boolean formulae in conjunctive and disjunctive normal form, to the majority function, to graphs with large connected components, and to a neural network with ...
We present a simple combinatorial criterion for determining concept classes that cannot be learned in the sense of Valiant from a polynomial number of positive-only examples. ...
With no restrictions on the form of the learned concepts the learnability of a concept class C implies the learnability of all concept classes C' C C. ...
doi:10.1007/bf00115896
fatcat:uanjanh4rvauld7hawr57purti
On the limits of proper learnability of subclasses of DNF formulas
1997
Machine Learning
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Second, we show that read-thrice DNF formulas are not properly learnable in the extended PAC model, assuming RP 5& NP. ...
As a further application of these techniques, we consider read-thrice DNF formulas. ...
On the other hand, it has been shown that for any constant k, k-term DNF formulas are learnable as k-CNF formulas (Valiant, 1984) , and k-term DNF formulas are learnable as k-terra DNF formulas when the ...
doi:10.1007/bf00114011
fatcat:6c66z2yse5ff3gx7nmdqmsrum4
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