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Page 408 of Mathematical Reviews Vol. 49, Issue 2
[page]

1975
*
Mathematical Reviews
*

*Prefix*

*classes*

*of*

*Krom*

*formulas*. J. Symbolic Logic 38 (1973), 628-642. ... Logik Grundlagen Math. 19 (1973), 117-126, The

*class*

*of*Kr

*of*

*Krom*

*formulas*consists

*of*those

*formulas*

*of*first-order predicate calculus that become conjunctions

*of*two-termed disjunctions

*of*signed atomic ...

##
###
Page 5433 of Mathematical Reviews Vol. , Issue 86m
[page]

1986
*
Mathematical Reviews
*

Let

*Krom*denote the*class**of**Krom**formulas*, Sat the*class**of*all satisfiable*formulas*, and for a regular expression w over {3,V}, let w denote the*class**of**formulas*with*prefix*w. ... The main results*of*this paper are as follows: (1) V3VN Kromn Sat € P, whereas the*class**of*unsatisfiable*formulas*in V3VN*Krom*is complete for nondeterministic logarithmic space. ...##
###
Page 4802 of Mathematical Reviews Vol. , Issue 83m
[page]

1983
*
Mathematical Reviews
*

A positive solution is given for the decision problem for the

*class**of**formulas**of*Kr~ with*prefixes**of*the form V3V. M. R.*Krom*(Davis, Calif.) Parker-Rhodes, A. ... The*class**of**formulas*in Kr~ with*prefixes**of*the form V3V3 and the*class**of**formulas*in Kr~ with*prefixes**of*the form VVV3I are both shown to have unsolvable decision problems. ...##
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Capturing complexity classes by fragments of second-order logic

1992
*
Theoretical Computer Science
*

The fragments are second-order Horn logic, second-order

doi:10.1016/0304-3975(92)90149-a
fatcat:gkyqqyzxgjctxg6vdvndaumgyy
*Krom*logic as well as a symmetric and a deterministic version*of*the latter. ... ., Capturing complexity*classes*by fragments*of*second-order logic, Theoretical Computer Science 101 (1992) 35-57. ... Preliminary versions have appeared in the proceedings*of*the 8th Symposium on Theoretical Aspects*of*Computer Science, STACS 9 1, Hamburg, February 199 1, and*of*the 6th IEEE Conference on Structure in ...##
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The complexity of the satisfiability problem for Krom formulas

1984
*
Theoretical Computer Science
*

For example, we show that determinmg satisfiability

doi:10.1016/0304-3975(84)90138-5
fatcat:pvr35qs3tjgubnqw4elb6sejoa
*of**Krom**formulas*with quantifier*prefix**of*the form 3. .3V. . ... We study the computational complexity*of*the satisfiability problem for*Krom*rf'Nf L,*formulas*. ... In this section we show only that satlsfi&ility*of*a monadic*Krom**formula*with arbitrary quantifier*prefix*can be tested i4 polynomial time. ...##
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Page 1822 of Mathematical Reviews Vol. , Issue 83e
[page]

1983
*
Mathematical Reviews
*

It is proved that the

*prefix**classes*3V3V, V33V, VW3V, V3VV*of**Krom**formulas*(‘hese are all the*classes**of**Krom**formulas*for which the decision problem for satisfiability is known to be unsolvable) are ... (An effective mapping g*of*all*formulas*to a*class*C*of**Krom**formulas*is called a conservative reduction if, for each*formula*F, (i) F is satisfiable if and only if p( F) is satisfiable; (ii) F has a finite ...##
###
Book Review: The decision problem: Solvable classes of quantificational formulas

1982
*
Bulletin of the American Mathematical Society
*

Unsolvable

doi:10.1090/s0273-0979-1982-15033-9
fatcat:tw3fcc3psfbnpd6eej2j3qizty
*classes**of*quantificational*formulas*, by Harry R. Lewis, Addison-Wesley, Reading, Mass., 1979, xv + 198 pp., $13.50. What is the decision problem in question? ... (A*class*C*of*sentences is called a reduction*class*for satisfiability if there is an algorithm assigning a sentence 5" in C to any first-order sentence S in such a way that S' is satisfiable if and only ... known by 1979, on*prefix*-similarity-*Krom**classes*, on*prefix*-similarity-Horn*classes*, and on a couple*of*other programs. ...##
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Page 015 of Mathematical Reviews Vol. , Issue 81I
[page]

1981
*
Mathematical Reviews
*

form

*of*their matrix. (2) The decision problem for all solv- abie*prefix**classes*, i.e.*classes**of**formulae*determined by the form*of*their*prefix*. (3) Finite controllability (“is every satisfiable for ... for all*classes*treated in (1) and (2). (4) The decision problem and finite control- lability for the Maslov*class**of**formulae*specified by*prefix*and truth-functional restrictions (namely, the*prefix*...##
###
Do Hard SAT-Related Reasoning Tasks Become Easier in the Krom Fragment?
[article]

2018
*
arXiv
*
pre-print

We thus also consider the CardMinSat problem with respect to additional restrictions to

arXiv:1711.07786v2
fatcat:darioyhufbcqbazbuiykrn5bbm
*Krom**formulas*towards a better understanding*of*the tractability frontier*of*such problems. ... We will make use*of*this fact to study the complexity*of*reasoning tasks in belief revision and logic-based abduction and show that, while in some cases the restriction to*Krom**formulas*leads to a decrease ... . , v m )*of*the lexicographically maximal (*prefix**of*a possible) model*of*ϕ. ...##
###
Page 260 of Mathematical Reviews Vol. 50, Issue 2
[page]

1975
*
Mathematical Reviews
*

The proof uses an effective mapping

*of*register machines and their behavior into the*prefix**class**of**Krom**formulas*mentioned first. ... The author considers the decision problem for the special*class*Kr*of**Krom**formulas*, i.e., prenex normal*formulas*whose propo- sitional matrix is a conjunctive normal form whose disjunctions are binary ...##
###
Page 1144 of Mathematical Reviews Vol. , Issue 87c
[page]

1987
*
Mathematical Reviews
*

The author considers the

*prefix**classes*3V3™, 3V73°°(=], V3V3~, Wa, VWa~v, VvVa~Vv[*Krom*9 Horn], Vav3~°[*Krom*Horn], 3v73 [*Krom*M Horn], ¥°3°(*Krom*]*of*the*formulas**of*first-order predicate logic with only ... He shows that the satisfiability [in finite models]*of*the*formulas**of*the theory*of*types is reducible to the satisfiability*of**formulas*from these*classes*in the set N*of*natural numbers [in a segment ...##
###
Enumeration Classes Defined by Circuits
[article]

2022
*
arXiv
*
pre-print

In this way we obtain a framework to distinguish between the complexity

arXiv:2205.00539v1
fatcat:ovk5b3gy2jfuzkrlb5u33lplqa
*of*different problems known to be in 𝐃𝐞𝐥𝐚𝐲𝐏, for which a formal way*of*comparison was not possible to this day. ... ., from graph theory, Gray code enumeration, and propositional satisfiability in our*classes*. ... We would like to mention in particular the maybe algorithmically most interesting contribution*of*our paper, the case*of*enumeration for satisfiability*of*2-CNF (*Krom*)*formulas*. ...##
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On the Complexity of Horn and Krom Fragments of Second-Order Boolean Logic
[article]

2020
*
arXiv
*
pre-print

*Of*the second sort, we consider Horn,

*Krom*, and core fragments

*of*the Boolean matrix. We classify the complexity

*of*logics obtained by combining these two types

*of*restrictions. ... Furthermore, we establish NL-completeness for the

*Krom*and core fragments, when k=1 and both restrictions

*of*the first sort are in effect. ...

*prefix*. ...

##
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Resolution Strategies as Decision Procedures

1976
*
Journal of the ACM
*

(without producing the empty clause) when apphed to satisfiable

doi:10.1145/321958.321960
fatcat:2h3w5icvb5drhpt6h3tk6vd7sm
*formulas*in certain*classes*provide new, and in some cases more enlightening, demonstrations*of*the solvablhty*of*these*classes*A technique ... There are, however, well-known and easily specified*classes**of**formulas*, called solvable*classes*, for which the question*of*satisfiabflity or unsatisfiability can be effectively decided; many solvable ... (*Krom*matrix) and*prefix*(3"V'3") that causes the solvability*of*the Maslov*class*. ...##
###
Expressing versus Proving: Relating Forms of Complexity in Logic

2010
*
Journal of Logic and Computation
*

In particular, a composition or a Boolean combination

doi:10.1093/logcom/exq008
fatcat:lpla27ghunf5fmmvdanaoasaei
*of*problems in the*class*is usually still within the same*class*(with the notable exception*of*complementation: for non-deterministic time*classes*... with different computational models often give the same*class**of*algorithms. ... I am very grateful to him for suggesting many*of*the ideas, as well as the framework in which these connections became natural. ...
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