N. Immerman, "Languages which Capture Complexity Classes", Proc. of 15th ACM Symposium on Theory of Computing, 1983, 347-354.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....it was proven that the NPTIME computable queries are precisely the queries expressible in existential second order logic. ffl In [V82] it was proven that (given an ordering) the PSPACE computable queries are precisely the queries expressible in While (renamed PFP in [AbV91] ffl In [V82] and [I83], it was proven that the PTIME computable queries are precisely the queries expressible in (positive elementary) fixed point logic (given an ordering) ffl In [I87] it was proven that the NLOGSPACE computable queries are precisely the queries expressible in transitive closure logic (given an ....

....(x; y) is equivalent to the distance from x to y is at most , so that 1 is the binary Graph Reachability query. Thus we have the boolean query, 0 ( j 8x; y [9path from x to y] and the induction closes in d 1 iterations, where d is the diameter of the graph. Remark 1. 1 It turns out ([I83]) that on finite structures, the class of FO pos LFP expressible queries is closed under negation. Thus without loss of generality we can refer to this logic as FO LFP. One critical point. It is not hard to show that the graph has an even number of vertices cannot be expressed in FO LFP. ....

[Article contains additional citation context not shown here]

N. Immerman, Languages which capture complexity classes, Proc. 15th ACM Symp. Theory of Comp. (STOC'83), 347--354.

....(TC) operator rather than least xed point. That is, nondeterministic logspace is the class of problems de nable in rst order logic with the addition of TC (see Immerman [Imm88] And if one replaces rst order logic with TC with second order logic with TC the result is PSPACE (see Immerman [Imm83] Other, analogous results in this eld go on to characterize various circuit and parallel complexity classes, the polynomial time hierarchy, and other space classes, and even yield results concerning counting classes. The intuition provided by looking at complexity theory in this way has ....

N. Immerman. Languages which capture complexity classes. In Proc. 15th Symposium on Theory of Computation, pages 760-778. ACM Press, 1983.

....trees and forests have treewidth 1, series parallel graphs and outerplanar graphs 2, almost trees with k additional edges have treewidth k 1, Halin graphs g 3, and members of k terminal recursive graph families have treewidth k. More information on these classes can be found in [11, 27]. At the same time, similar graph measures were found and suggested as a generalization of being series parallel, and also linear time algorithms were found for these graph families and other previously known families of graphs. For a survey of this activity see Johnson [27] Particularly, the ....

....can be found in [11, 27] At the same time, similar graph measures were found and suggested as a generalization of being series parallel, and also linear time algorithms were found for these graph families and other previously known families of graphs. For a survey of this activity see Johnson [27]. Particularly, the property of being a subgraph of a k tree was suggested in [6] and shown equivalent to having treewidth k by Scheffier [37] and Wimer [43] A See [43] the statement assumes that all the basis graphs in the definition, with edges added between all pairs of terminals, also ....

H. IMMERMAN, Languages which capture complexity classes, SIAM J. Comput. 4 (1987), 760-778.

....our previous observation that unique integers can be assigned to derived tuples once non deterministic constructs are available thus attaching an ordering to domains. It is known that deterministic languages on ordered domains are more powerful than deterministic languages on unordered domains [Imm87]. The objective of this paper is to revisit the issue of non deterministic extensions to Horn clause based languages from the viewpoints of expressive power and amenability to e#cient implementation. We show that the current proposal, namely the choice proposal described in [KN88] and [NT89] ....

Immerman, N., Languages which Capture Complexity Classes, SIAM J. Computing, 16,4, pp. 760-778, 1987.

....and those were all cases in which the target of a plugging operation was not reduced. For cases when the order does not matter, the operations may also be performed in parallel. Indeed, we suspect that UPSILON is usefully closer to modeling parallel complexity theory than other calculi. Immerman [Imm87, Imm89] and others including [CH82] have demonstrated that low level parallel complexity classes correspond to first order formal systems, and that possession of a total ordering matters in the analysis. To implement complexity analysis, we need to introduce some input and output conventions to UPSILON, ....

N. Immerman. Languages which capture complexity classes. SIAM Journal on Computing, 16:760--778, 1987. 25

.... of Hartmanis and Stearns, On the Computational Complexity of Algorithms [60] Many textbooks cover this material, for example [75] The extension of this theory to higher order objects is an active field [99] and the study of feasible computation is another active area related to this article [12, 69, 72, 73, 74]. These topics are covered also in Schwichtenberg [13] and in the articles of Jones [70] Schwichtenberg [98] and Wainer [87] in this book. The work reported here is new and based largely on Constable and Crary [38] and Benzinger [14] as well as examples from Kreitz and Pientka [90] One ....

N. Immerman. Languages which capture complexity classes. SIAM Journal of Computing, 16:760--778, 1987.

....non deterministic game with space bound S(n) greater or equal to log(n) can be decided in non deterministic space S(n) Proof: The proof for win outcome problem follows from Definition 3.4.3 of non deterministic game. The proof for non loss outcome follows from definitions and Immerman s result [33, 34] non deterministic space O(S(n) co nondeterministic space O(S(n) 2 Now we can apply Savitch s result [35] that NSPACE(S(n) DSPACE(S(n) 2 ) and conclude the following corollary : Corollary 4.1.1 Any win, non loss, and Markov(m(n) outcome of non deterministic game with space bound S(n) ....

....play of game G , team T 0 must move by strategy oe 0 , and the players of T 1 must move by strategy oe 1 . By Proposition 4.1.2, the win (non loss) outcome of the game G N can be decided nondeterministic (co nondeterministic) space EXP k (O(S(n) 2 Corollary 5.2. 2 By the result of Immerman [33, 34], the non loss outcome of the game G N can be decided non deterministic space EXP k (O(S(n) Proof: The corollary follows from Immerman s result [33, 34] that: NSPACE(O(S(n) co Gamma NSPACE(O(S(n) 2 The above Theorem 5.2.3 and Corollary 5.2.2 lead to the following result. Corollary ....

[Article contains additional citation context not shown here]

N. Immerman, "Languages which capture complexity classes", in Proceedings of 15th Annual ACM Symposium on Theory of Computing, pages 347-354, May 1983.

....NP if is existential second order 7 (Fagin [39] where again is xed and S is the input. Conversely, every NP property can be described in this way. More generally, a property belongs to the polynomial hierarchy i it can be described by a second order formula (see Stockmeyer [60] Immerman [46] or Abiteboul et al. 1] If C = fSg where S is in nite, then the L theory of C may be undecidable. However the study of the theories of in nite structures and especially of their monadic (second order) theories is a very rich topic that we cannot even touch here. We refer the reader to survey ....

: IMMERMAN N., Languages which capture complexity classes, SIAM J. Comput. 16 (1987) 760-778.

....in B are existential. Such a graph is called an alternating graph or an ANDnOR graph. Then apath(x; y) holds if and only if 1. x = y, or 2. x is existential and there is a z with (x; z) 2 E and apath(z; y) or 3. x is universal and for all z with (x; z) 2 E, apath(z; y) holds. Reference: [CKS81, Imm81, Imm83] Hint: Reduce AM2CVP (Problem A.1.4) to AGAP. Create two existential nodes 0 and 1. Put edge (x i ; 0) into E if input x i is 0, and edge (x i ; 1) into E if input x i is 1. and gates are universal nodes and or gates are existential nodes. Inputs to a gate correspond to children in the ....

N. Immerman. Languages which capture complexity classes (preliminary report) . In Proceedings of the Fifteenth Annual ACM Symposium on Theory of Computing, pages 347--354, Boston, MA, April 1983.

.... applied by Scott to program semantics [69] have been used by Cocke and Schwartz [13] Kildall [44] Tenenbaum [77] and others [36, 42, 16, 67, 43, 74] to specify and implement global program analysis problems, are important to program verification [16, 17, 20, 23] arise in complexity theory [79, 39, 40, 33, 35, 59], and are used to support high level program transformations [2, 29, 7, 49, 62, 53, 56, 11, 54, 70, 60, 81, 51] We are further encouraged by the following facts: Any set generated by inductive definitions can also be defined as the least fixed point of a monotone function [1] Without a ....

Immerman, N. Languages Which Capture Complexity Classes. Proc. 15th ACM Symp. on Theory of Computing, April, 1983, pp. 347-354.

....This logic is generated by the set of all extended vectorizations Q k , k 1, of quanti ers Q in Q (see Section 2.3 for a de nition) The signi cance of vectorization has been recognized from the beginning in studies concerning logical characterizations of complexity classes. Immerman [Imm86, Imm87] de ned three di erent versions of transitive closure operator, and proved that they capture LOGSPACE, NLOGSPACE and PTIME, respectively. Later Stewart [Ste91, Ste92] proved that the Hamiltonian path operator, as well as some other NP complete operators, captures NP. In all these characterizations ....

N. Immerman. Languages which capture complexity classes. SIAM Journal on Computing, 16(4):760-778, 1987.

.... particularly with certain extensions of first order logic by various kinds of inductive definitions (see Immerman [13] for a survey) Pure first order logic per se appeared more recently in the context of low level parallel complexity classes in the paper by Gurevich and Lewis [11] Immerman [12] characterized the nonuniform complexity class AC 0 by the first order logic with all numerical predicates considered as logical relations. Note that in the previously mentioned characterizations, the linear order is usually present as a logical relation. This This work has been partially ....

Immerman, N., Languages which capture complexity classes, SIAM J.Comput., 16:4, 760--778, 1987.

....between the codes of n tuples of sets and n tuples of codes of the same sets from the point of view of Sub PTIME computability. It proves that defining Sub PTIME computability over HF and corresponding notion of definability is more problematic task than in the case of flat data bases [14, 17, 18]. More precisely, our reduction of the nested case to the flat one involves some peculiar technical problems and considerations, especially for the case of Sub PTIME. The main reason for this is a higher abstract level of HF sets in comparison with the first order finite structures. In fact, ....

....The main reason for this is a higher abstract level of HF sets in comparison with the first order finite structures. In fact, we reduce various versions of Delta language to the language of firstorder logic with a transitive closure operator FO Omega over finite graphs. It was shown by N. Immerman [17] that in the presence of a linear order (OE) this language (even closed under negations [18] cf. also [41] exactly corresponds to NLOGSPACE. It is also used an analogous description of DLOGSPACE, i.e. deterministic LOGSPACE [17] The description of PTIME computability over HF mentioned above ....

[Article contains additional citation context not shown here]

Immerman, N.: Languages which captures complexity classes. SIAM J. Comput., 16 4 (1987) 760--778

....This logic is generated by the set of all extended vectorizations Q k , k 1, of quantifiers Q in Q (see Section 2.3 for a definition) The significance of vectorization has been recognized from the beginning in studies concerning logical characterizations of complexity classes. Immerman [Imm86, Imm87] defined three different versions of transitive closure operator, and proved that they capture LOGSPACE, NLOGSPACE and PTIME, respectively. Later Stewart [Ste91, Ste92] proved that the Hamiltonian path operator, as well as some other NP complete operators, captures NP. In all these ....

N. Immerman. Languages which capture complexity classes. SIAM Journal on Computing, 16(4):760--778, 1987.

....those in B are existential. Such a graph is called an alternating graph or an ANDnOR graph. Then apath(x; y) holds if and only if 1. x = y, or 2. x is existential and there is a z with (x; z) 2 E and apath(z; y) or 3. x is universal and for all z with (x; z) 2 E, apath(z; y) holds. Reference: [CKS81, Imm81, Imm83] Hint: Reduce AM2CVP (Problem A.1.4) to AGAP. Create two existential nodes 0 and 1. Put edge (x i ; 0) into E if input x i is 0, and edge (x i ; 1) into E if input x i is 1. and gates are universal nodes and or gates are existential nodes. Inputs to a gate correspond to children in the ....

N. Immerman. Languages which capture complexity classes (preliminary report) . In Proceedings of the Fifteenth Annual ACM Symposium on Theory of Computing, pages 347--354, Boston, MA, April 1983.

....the processors implementing the algebra need not be powerful, as they are only required to perform very specific, simple operations on tuples. In fact, it is sufficient to have processors that can implement the basic Boolean circuit operations. This fact is formalized by a result due to Immerman [Imm87] stating that FO is included in AC 0 , the class of problems solvable by circuits of constant depth and polynomial size, with unbounded fan in. In conclusion, logic has proven to be a spectacularly effective tool in the database area. FO provides the basis for the standard query languages, ....

N. Immerman. Languages which capture complexity classes. SIAM J. on Computing, 16(4):760--778, 1987.

....the processors implementing the algebra need not be powerful, as they are only required to perform very specific, simple operations on tuples. In fact, it is sufficient to have processors that can implement the basic Boolean circuit operations. This fact is formalized by a result due to Immerman [Imm87] stating that FO is included in AC 0 , the class of problems solvable by circuits of constant depth and polynomial size, with unbounded fan in. In conclusion, logic has proven to be a spectacularly effective tool in the database area. FO provides the basis for the standard query languages, ....

N. Immerman. Languages which capture complexity classes. SIAM J. on Computing, 16(4):760--778, 1987.

....with successor is the first such completeness result involving what could be called a natural problem. Not withstanding the preceding paragraph, to our mind, our actual proof of Theorem 1 is the most interesting aspect of this note given that it is essentially identical to Immerman s proof in [10] that transitive closure logic (or, as was proven there, the positive version, TC [FO s ] has a normal form, except that in the combinatorial construction we replace an edge in one of Immerman s digraphs with a particular gadget (see the proof of Theorem 1) This fact encourages one to view ....

N. Immerman, Languages which capture complexity classes, SIAM J. Comput. 16 (1987) 760--778.

No context found.

N. Immerman, "Languages which Capture Complexity Classes", Proc. of 15th ACM Symposium on Theory of Computing, 1983, 347-354.

No context found.

H. Immerman. Languages which capture complexity classes. SIAM J. Comput., 4:760--778, 1987.

No context found.

N. Immerman, Languages which capture complexity classes, Proc. 15th Annual ACM Symp. on the Theory of Computing (1983) 347-354.

No context found.

N. Immerman, Languages which Capture Complexity Classes. SIAM J. Computing, 16,4, (1987). pp. 760-778.

No context found.

N. Immerman, Languages which Capture Complexity Classes. SIAM J. Computing, 16,4, (1987). pp. 760-778.

No context found.

Immerman N., Languages which Capture Complexity Classes. SIAM J. Computing, 16(4) (1987) p. 760-778.

No context found.

Immerman, N., Languages which Capture Complexity Classes, in: 15th Symposium on Theory of Computing, Association for Computing Machinery (1983), pp. 347-354.

First 50 documents

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC