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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.  ... 

Capturing complexity classes by fragments of second-order logic

Erich Grädel
1992 Theoretical Computer Science  
The fragments are second-order Horn logic, second-order 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  ... 
doi:10.1016/0304-3975(92)90149-a fatcat:gkyqqyzxgjctxg6vdvndaumgyy

The complexity of the satisfiability problem for Krom formulas

Larry Denenberg, Harry R Lewis
1984 Theoretical Computer Science  
For example, we show that determinmg satisfiability 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.  ... 
doi:10.1016/0304-3975(84)90138-5 fatcat:pvr35qs3tjgubnqw4elb6sejoa

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

Yuri Gurevich
1982 Bulletin of the American Mathematical Society  
Unsolvable 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.  ... 
doi:10.1090/s0273-0979-1982-15033-9 fatcat:tw3fcc3psfbnpd6eej2j3qizty

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]

Nadia Creignou, Reinhard Pichler, Stefan Woltran
2018 arXiv   pre-print
We thus also consider the CardMinSat problem with respect to additional restrictions to 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.  ... 
arXiv:1711.07786v2 fatcat:darioyhufbcqbazbuiykrn5bbm

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]

Nadia Creignou, Arnaud Durand, Heribert Vollmer
2022 arXiv   pre-print
In this way we obtain a framework to distinguish between the complexity 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.  ... 
arXiv:2205.00539v1 fatcat:ovk5b3gy2jfuzkrlb5u33lplqa

On the Complexity of Horn and Krom Fragments of Second-Order Boolean Logic [article]

Miika Hannula, Juha Kontinen, Martin Lück, Jonni Virtema
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.  ... 
arXiv:2007.03867v1 fatcat:rwno7wxn2rcqddb5n35vafvaty

Resolution Strategies as Decision Procedures

William H. Joiner
1976 Journal of the ACM  
(without producing the empty clause) when apphed to satisfiable 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.  ... 
doi:10.1145/321958.321960 fatcat:2h3w5icvb5drhpt6h3tk6vd7sm

Expressing versus Proving: Relating Forms of Complexity in Logic

A. Kolokolova
2010 Journal of Logic and Computation  
In particular, a composition or a Boolean combination 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.  ... 
doi:10.1093/logcom/exq008 fatcat:lpla27ghunf5fmmvdanaoasaei
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