P.C. Kanellakis. Elements of Relational Database Theory. Handbook of Theoretical Computer Science, (J. van Leeuwen editor), volume B, chapter 17, 1073-- 1158, North-Holland, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....recursive queries, and to establish connections with known results about datalog. For example, the restricted form of the datalog programs needed to express path queries (linear datalog) immediately yields an upper bound of nc for the complexity of path queries, using known results about datalog [19] (note however that the earlier direct algorithm establishes the better nlogspace data complexity) 2.3 Path queries and datalog We show how path queries can be expressed as linear datalog programs with monadic idb s. We assume familiarity with datalog (e.g. see [4] Let p be a regular ....

....state h (x) for each accepting state h The datalog programs that are obtained (by either the quotient or state approach) are very particular. First, they are linear, i.e. at most one intensional predicate occurs in the body of each rule. Since the evaluation of linear datalog programs is in nc [19], it follows that the evaluation of path queries is also in nc. The programs are also monadic [19] the recursion is over a unary predicate) another restriction of datalog programs of importance in query optimization. Remark 2.1 (Infinite Web) The point of view that the Web is infinite is ....

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P. C. Kanellakis. Elements of Relational Database Theory. Handbook of Theoretical Computer Science, Elsevier, 1991, pages 1074--1156.

....section, we define the effective fragments of infinitary logics and relate them to relational machines. The connection with restricted query languages, yielding characterizations in language theoretic terms, is considered in Section 4. 2 Preliminaries We assume basic knowledge of databases [K90, U88] and formal language theory [HU79] In databases, only finite structures are considered. Most traditional query languages are based on first order logic without function symbols (here FO) The simplicity of Codd s algebraization of FO and the fact that FO is in (uniform) AC 0 [BIS90] and, thus, ....

Kanellakis, P.C., Elements of Relational Database Theory, Handbook of Theoretical Computer Science (J. van Leeuwen, A.R. Meyer, N. Nivat, M.S. Paterson, and D. Perrin, eds.), Vol. B, Chapter 17, North-Holland, 1990.

.... good books on firstorder logic, for example [53] or good surveys on constraint logic programming and fixpoint semantics [42, 75, 153, 154] There are also good introductions to logic programming (without constraints) in [10, 50, 101] and to database query languages (also without constraints) in [3, 79, 149]. One can also find an earlier tutorial on constraint databases in [80] and an applications oriented survey in [61] Points 1(b) and 1(c) will be illustrated by a new algebra for constraint databases with integer order constraints. It also analyses the computational complexity of evaluating ....

....we can see that two important requirements have to be met. First, each query must terminate. Second, each query must give as output a database. We might call these the termination and the constructibility requirements. Both of the above requirements are satisfied in the relational data model [41, 3, 79, 149], which is illustrated in Figure 1. Each relational database is a finite set of tables. Each table is an abstract data type and is a relation containing a finite set of tuples. A requirement in the relational data model is that queries be evaluable functions from finite databases to finite ....

[Article contains additional citation context not shown here]

P.C. Kanellakis. Elements of Relational Database Theory. Handbook of Theoretical Computer Science, Vol. B, chapter 17, (J. van Leeuwen editor), North-Holland, 1990.

....are listed in Section 5. 2 Basic Concepts Our work will be a particular generalization of Codd s relational database model [3] and the language Datalog. We assume that the reader is familiar with these concepts and their relevance to databases. An introduction to these can be found for example in [16, 28]. In this section we will give only the necessary definitions for the new generalizations of relational databases and Datalog. Generalized relational databases: Our database framework is set up as follows. Let A(x 1 ; x k ) be a relation symbol with arity k. Let t 2 Z k be any sequence ....

....head of the rules. We make this requirement to allow the possibility of compiler and run time optimizations. We know that many good optimization methods for relational database languages are based on bottom up evaluation. For more about optimization and the importance of bottom up evaluation see [16, 28]. Safety: Recall that an assumption in Codd s relational model is that relations (both input and output) are always finite structures, that is, they are always composed of a finite number of relational tuples. This is called the safety requirement. Analogous to that requirement, in our extension ....

[Article contains additional citation context not shown here]

P.C. Kanellakis. Elements of Relational Database Theory. Handbook of Theoretical Computer Science, Vol. B, chapter 17, (J. van Leeuwen, A.R. Meyer, N. Nivat, M.S. Paterson, D. Perrin editors), North-Holland, 1990.

.... power [AU79, GM78, Zl76] Since then, many higherorder query languages have been investigated [AV89, CH80, Ch81, CH82, Im86, Va82] A query language that has received considerable attention is Datalog, the language of logic programs (known also as Horn clause programs) without function symbols [Ka90, Ul89], which is essentially a fragment of fixpoint logic [CH85, Mo74] The gain in expressive power does not, however, come for free; evaluating Datalog programs is harder than evaluating first order queries [Va82] Recent works have addressed the problems of finding efficient evaluation methods for ....

Kanellakis P.C.: Elements of Relational Database Theory. Handbook of Theoretical Computer Science, Vol. B, Chapter 17, J. van Leeuwen, A.R. Meyer, N. Nivat, M.S. Paterson, D. Perrin ed., NorthHolland 1990.

.... unrestricted relation, for finite or infinite sets of points in a k dimensional space [24] In particular, it was shown that relational calculus is identical to relational algebra for countable domains and that relational algebra for infinite relations is exactly the same as for finite relations [25] 6 . Therefore, the relational framework we have presented applies as is to infinite relations. In this section we will demonstrate the applicability of our results to the special case of linear inequalities over infinite domains like the Rationals as well as over finite and infinite subsets of ....

P. Kanellakis, Elements of Relational Database Theory, Handbook of Theoretical Computer Science, Chapter 17, Vol, B, J. van Leeuwen editor, North-Holland, 1990.

....them to relational machines in Section 3. We consider a generalization to untyped machines in Section 4. The connection with restricted query languages, yielding characterizations in language theoretic terms, is considered in Section 5. 2 Preliminaries We assume basic knowledge of databases [K90, U88] and formal language theory [HU79] In this section, we define the infinitary logics L1 and L 1 [Ba77] and briefly present the database languages and computational devices that are considered in the paper, namely, fixpoint, while, and relational machines. A database schema oe is a finite ....

Kanellakis, P.C., Elements of Relational Database Theory, Handbook of Theoretical Computer Science (J. van Leeuwen, A.R. Meyer, N. Nivat, M.S. Paterson, and D. Perrin, eds.), Vol. B, Chapter 17, North-Holland, 1990.

....the presentation. Consequently, the exposition is informal. As an attenuating circumstance, we invoke the modest The author was supported in part by NSF Grant IRI 9221268. 2 VICTOR VIANU aims of the paper: to give a flavor of the database area, and to incite curiosity. We refer the reader to [Kan91, AHV95] for more detailed and somewhat formal presentations of database theory. Early database theory is covered in [Mai83] A concise overview of the field aimed at computer science theoreticians is also provided in [Yan95] The relationship of database theory and practice is explored in ....

.... some time, such as the decidability of implication for the class of embedded multi valued dependencies [Fag77] The question was recently settled in the negative [Her95] Comprehensive presentations of dependency theory can be found in [Var87, FV86] A more concise presentation is provided in [Kan91] Dependency theory is also the topic of the book [Tha91] 3.3. Update Languages. The content of a database changes over time. This raises a host of problems related to dynamic aspects of databases, not usually considered in finite model theory. The first question is to provide languages for ....

P. C. Kanellakis, Elements of relational database theory, Handbook of Theoretical Computer Science (J. Van Leeuwen, ed.), Elsevier, 1991, pp. 1074--1156.

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P.C. Kanellakis. Elements of Relational Database Theory. Handbook of Theoretical Computer Science, (J. van Leeuwen editor), volume B, chapter 17, 1073-- 1158, North-Holland, 1990.

....rules (resp. one rule and a projection) and one initialization rule, where all predicates have small arities (6 or 7) 1 Introduction It has been realized for some time that first order database query languages are lacking in expressive power. This has led to the study of Datalog programs [BR88, K90, U89], which combine positive existential first order formulas with recursion see [CH85] Analyzing the depth of recursion of these database logic programs has emerged as a fundamental problem, e.g. for parallel evaluation [CK86, K88, UV88] or for optimization [N89b] Datalog boundedness (i.e. ....

P.C. Kanellakis, Elements of Relational Database Theory, Handbook of Theoretical Computer Science, Vol. B, Chapter 17, J. van Leeuwen, A.R. Meyer, N. Nivat, M.S. Paterson, D. Perrin ed., North-Holland 1990, 1073--1157.

....is undecidable for two linear rules (resp. one rule and a projection) one initialization rule and small arity predicates. 1 Introduction It has been realized for some time that first order database query languages are lacking in expressive power. This has led to the study of Datalog programs [K90, U89], which combine positive existential first order formulas with recursion see [CH85] Analyzing the depth of recursion of these database logic programs has emerged as a key problem, e.g. for parallel evaluation [CK86, K88, UV88] or for optimization [N89b, S88] Datalog boundedness (i.e. ....

P.C. Kanellakis, Elements of Relational Database Theory, Handbook of Theoretical Computer Science, Vol. B, Chapter 17, J. van Leeuwen, A.R. Meyer, N. Nivat, M.S. Paterson, D. Perrin ed., North-Holland 1990, 1073--1157.

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P.C. Kanellakis. Elements of Relational Database Theory. Handbook of Theoretical Computer Science, Vol. B, chapter 17, (J. van Leeuwen editor), North-Holland, 1990.

....for monadic and or recursion free method schemas, which happen to be decidable. We also quantify the effect of covariance, which is a widely used constraint on the signature of methods. For the various concepts used from complexity theory, see [15, 19, 20, 29] and from database theory, see [21, 30]. We briefly summarize our other results. Let n be the size of method definitions in the input method schema and c the size of the class hierarchy. In the case of monadic schemas, the set of possible computations can be described using a context free language. An inconsistency may be reached if ....

P.C. Kanellakis. Elements of Relational Database Theory. Handbook of Theoretical Computer Science, Vol. B, Chapter 17, (J. van Leeuwen, A.R. Meyer, N. Nivat, M.S. Paterson, D. Perrin editors), North-Holland, 1990.

.... [AU79, GM78, Zl76] Since then, many higher order query languages have been investigated [AV89, CH80, Ch81, CH82, Im86, Va82] A query language that has received considerable attention recently is Datalog, the language of logic programs (known also as Horn clause programs) without function symbols [K90, Ul89], which is essentially a fragment of fixpoint logic [CH85, Mo74] See [Ul88] for a detailed discussion of Datalog. The gain in expressive power does not, however, come for free; evaluating Datalog programs is harder than evaluating first order queries [Va82] Recent works have addressed the ....

Kanellakis P.C.: Elements of Relational Database Theory. Handbook of Theoretical Computer Science, Vol. B, Chapter 17, J. van Leeuwen, A.R. Meyer, N. Nivat, M.S. Paterson, D. Perrin ed., North-Holland 1990.

....the CQL framework from arbitrary (and inherently exponential) theorem proving [30, 9, 15] Example 1. Let us illustrate database querying and introduce some of its notation. The meaning and use is (or rather should be) intuitively obvious. For formal definitions we refer the reader to [40, 69]. To see that constraints should be part of any database query language consider an example from [41] This is a query program with Expenses, Savings and Income input relations, Balanced output relation, and a single linear equation constraint: x is user id, f is amount spent for food, r for ....

....spatial objects. For efficiency reasons we require that these constraints be quantifierfree, just like the CLP axioms are quantifier free. The [41] framework is thus one of complete information. The problem of managing partial information in databases has received a fair amount of attention, see [40] for pointers to the database literature. For example, formulas with variables called null values can be thought of as formulas representing many possible states (of which one is true) They would correspond to constraints that have existential quantifiers. In this sense, constraint programming ....

[Article contains additional citation context not shown here]

P.C. Kanellakis. Elements of Relational Database Theory. Handbook of Theoretical Computer Science, Vol. B, chapter 17, (J. van Leeuwen editor), North-Holland, 1990.

....relation by a finite set of generalized tuples need not be uniquely defined. Relational calculus constraints: We present a short but self contained description of the relational calculus with a given a class of constraints. For more details on the relational calculus in database theory see [15, 29, 54]. Definition 1.6 Let Phi be a class of constraints. Let R 1 ; R i ; be predicate symbols, each with a fixed arity. A relational calculus Phi query program is a formula of the first order predicate calculus with equality, such that its atomic formulas are (1) of the form R i (x ....

....x 2 g. The result (interpreting the generalized relation as an infinite set of points) of 9x:R(x; y) is the set fyjy 0g, which cannot be represented by polynomial equality constraints. 2 Datalog constraints: We now consider Datalog with constraints. The syntax is that of Datalog (e.g. see [1, 29, 33, 54, 55]) but we allow the bodies of rules to contain constraints. Definition 1.10 Let Phi be a class of constraints. Let R 1 ; R i ; be predicate symbols, each with a fixed arity. A Datalog Phi query program is a finite set of rules of the form: t 0 : t 1 ; t 2 ; t l : t 0 ....

[Article contains additional citation context not shown here]

P.C. Kanellakis. Elements of Relational Database Theory. Handbook of Theoretical Computer Science, Vol. B, chapter 17, (J. van Leeuwen editor), North-Holland, 1990.

....relation by a finite set of generalized tuples need not be uniquely defined. Relational calculus constraints: We present a short but self contained description of the relational calculus with a given a class of constraints. For more details on the relational calculus in database theory see [13, 27, 52]. Definition 1.6 Let Phi be a class of constraints. Let R 1 ; R i ; be predicate symbols, each with a fixed arity. A relational calculus Phi query program is a formula of the first order predicate calculus with equality, such that its atomic formulas are (1) of the form R i (x ....

....x 2 g. The result (interpreting the generalized relation as an infinite set of points) of 9x:R(x; y) is the set fyjy 0g, which cannot be represented by polynomial equality constraints. 2 Datalog constraints: We now consider Datalog with constraints. The syntax is that of Datalog (e.g. see [1, 27, 31, 52, 53]) but we allow the bodies of rules to contain constraints. Definition 1.10 Let Phi be a class of constraints. Let R 1 ; R i ; be predicate symbols, each with a fixed arity. A Datalog Phi query program is a finite set of rules of the form: t 0 : t 1 ; t 2 ; t l : t 0 ....

[Article contains additional citation context not shown here]

P.C. Kanellakis. Elements of Relational Database Theory. Handbook of Theoretical Computer Science, Vol. B, chapter 17, (J. van Leeuwen editor), North-Holland, 1990.

....for monadic and or recursion free method schemas, which happen to be decidable. We also quantify the effect of covariance, which is a widely used constraint on the signature of methods. For the various concepts used from complexity theory, see [15, 19, 20, 30] and from database theory, see [21, 31]. We briefly summarize our other results. Let n be the size of method definitions in the input method schema and c the size of the class hierarchy. In the case of monadic schemas, the set of possible computations can be described using a context free language. An inconsistency may be reached if ....

P.C. Kanellakis. Elements of Relational Database Theory. Handbook of Theoretical Computer Science, Vol. B, Chapter 17, (J. van Leeuwen, A.R. Meyer, N. Nivat, M.S. Paterson, D. Perrin editors), North-Holland, 1990.

....for two linear rules (resp. one rule and a projection) one initialization rule and small arity predicates (6 or 7) 1 Introduction It has been realized for some time that first order database query languages are lacking in expressive power. This has led to the study of Datalog programs [K90, U89], which combine positive existential first order formulas with recursion see [CH85] Analyzing the depth of recursion of these database logic programs has emerged as a fundamental problem, e.g. for parallel evaluation [CK86, K88, UV88] or for optimization [N89b] Datalog boundedness (i.e. ....

P.C. Kanellakis, Elements of Relational Database Theory, Handbook of Theoretical Computer Science, Vol. B, Chapter 17, J. van Leeuwen, A.R. Meyer, N. Nivat, M.S. Paterson, D. Perrin ed., North-Holland 1990, 1073--1157.

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P.C. Kanellakis. Elements of Relational Database Theory. Handbook of Theoretical Computer Science, J. van Leeuwen editor, volume B, chapter 17, pp. 1073--1158. North-Holland, 1990.

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