L.J. Stockmeyer. The Complexity of Decision Problems in Automata Theory. PhD thesis, Department of Electrical Engineering, MIT, 1974.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... n (l) to decide whether a structure of size n satisfies a firstorder sentence of size l, and under complexity theoretic assumptions, it can be proved that no real improvement is possible: The problem of deciding whether a given structure satisfies a given first order sentence is PSPACE complete [17, 19], and if parameterized by the size of the input sentence, it is complete for the parameterized complexity class AW[ 7] The latter result implies that it is unlikely that the problem is fixed parameter tractable (cf. 6] i.e. that it can be solved in time f(l) n c , for a function f and ....

L.J. Stockmeyer. The Complexity of Decision Problems in Automata Theory. PhD thesis, Department of Electrical Engineering, MIT, 1974.

.... (l) to decide whether a structure of size n satisfies a first order sentence of size l, and under complexity theoretic assumptions, it can be proved that no real improvement is possible: The problem of deciding whether a given structure satisfies a given first order sentence is PSPACE complete [18, 20], and if parameterized by the size of the input sentence, it is complete for the parameterized complexity class AW[ 7] The latter result implies that it is unlikely that the problem is fixed parameter tractable (cf. 6] i.e. that it can be solved in time f(l) n c , for a function f and ....

L.J. Stockmeyer. The Complexity of Decision Problems in Automata Theory. PhD thesis, Department of Electrical Engineering, MIT, 1974.

....the complexity theoretic considerations made in this paper. The natural parameterization of query evaluation is by the length of the input formula: PARAMETERIZED L EVALUATION Input: Formula 2 L, structure A. Parameter: jj jj Problem: Decide if (A) 6= FO EVALUATION is PSPACE complete [13], and PARAMETERIZED FO EVALUATION is complete for the parameterized complexity class AW[1] 5] which implies that it is W[1] hard. Conjunctive Queries. A conjunctive query is a first order formula of the form 9x 1 : 9x k 1 : n ) where 1 ; n are atoms. The class of ....

L.J. Stockmeyer. The Complexity of Decision Problems in Automata Theory. PhD thesis, Department of Electrical Engineering, MIT, 1974.

....the complexity theoretic considerations made in this paper. The natural parameterization of query evaluation is by the length of the input formula: PARAMETERIZED L EVALUATION Input: Formula 2 L, structure A. Parameter: jj jj Problem: Decide if (A) 6= FO EVALUATION is PSPACE complete [12], and PARAMETERIZED FO EVALUATION is complete for the parameterized complexity class AW[1] 5] which implies that it is W[1] hard. Conjunctive Queries. A conjunctive query is a rst order formula of the form 9x 1 : 9x k 1 : n ) where 1 ; n are atoms. The class of all ....

L.J. Stockmeyer. The Complexity of Decision Problems in Automata Theory. PhD thesis, Department of Electrical Engineering, MIT, 1974.

....the complexity theoretic considerations made in this paper. The natural parameterization of query evaluation is by the length of the input formula: PARAMETERIZED L EVALUATION Input: Formula 2 L, structure A. Parameter: jj jj Problem: Decide if (A) 6= FO EVALUATION is PSPACE complete [12], and PARAMETERIZED FO EVALUATION is complete for the parameterized complexity class AW[1] 5] which implies that it is W[1] hard. Conjunctive Queries. A conjunctive query is a first order formula of the form 9x 1 : 9x k Gamma ff 1 : ff n ) where ff 1 ; ff n are atoms. The ....

L.J. Stockmeyer. The Complexity of Decision Problems in Automata Theory. PhD thesis, Department of Electrical Engineering, MIT, 1974.

....fragments have the same expressive power as the well known guarded fragment and the finite variable fragments of first order logic, respectively. 1 Introduction Evaluating first order, or relational calculus, queries against a finite relational database is well known to be PSPACE complete [15]. The complexity we refer to here is called the combined complexity of the query language [19] i.e. the complexity of the evaluation problem is measured both in terms of the length of the query and the size of the database. Many research efforts went into handling this high worst case complexity. ....

L.J. Stockmeyer. The Complexity of Decision Problems in Automata Theory. PhD thesis, Department of Electrical Engineering, MIT, 1974.

....fragments have the same expressive power as the wellknown guarded fragment and the finite variable fragments of first order logic, respectively. 1 Introduction Evaluating first order, or relational calculus, queries against a finite relational database is well known to be PSPACE complete [17]. The complexity we refer to here is called the combined complexity of the query language [21] i.e. the complexity of the evaluation problem measured both in terms of the length of the query and the size of the database. Many research efforts went into handling this high worst case complexity. In ....

....12. od It is easy to see that this procedure works correctly; using (1) Fact 1, and Fact 2 we get the desired time bound. 2 Remark 4.3. The function f in the statement of Theorem 4.2 is essentially determined by the size of the automaton to which the input formula is translated. It is well known [17] that there is no elementary bound on the size of the automaton in terms of the size of the formula. The main factor contributing to the large automaton size is the number of quantifier alternations in the formula; roughly there is one iterated exponential per quantifier alternation. However, ....

L.J. Stockmeyer. The Complexity of Decision Problems in Automata Theory. PhD thesis, Department of Electrical Engineering, MIT, 1974.

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