Richard E. Ladner. The computational complexity of provability in systems of modal propositional logic. SIAM J. Computing, 6:467--480, 1977. Home/Search Document Not in Database Summary Related Articles Check |
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An O((n.log n)³)-time transformation from Grz into.. - Demri, Goré (1998) (Correct)
....alphabet. By definition (see e.g. 23] for any fragment of classical logic that is C hard with respect to C many one reductions , there is a mapping f in C such that any modal formula OE 2 L iff f(OE) is valid in such a first order fragment. From the facts that G is in PSPACE (see e.g. [2, 15]) validity in FO 2 is NEXPTIME hard [8] and PSPACE NEXPTIME, it is easy to conclude that there exists a polynomial time transformation from G into validity in FO 2 . As is well known, this illustrates the difference between the fact that a propositional modal logic K OE is characterised by a ....
R. Ladner. The computational complexity of provability in systems of modal propositional logic. SIAM Journal of Computing, 6(3):467--480, September 1977.
Modal Logics for Parallelism, Orthogonality, and Affine.. - Balbiani, Goranko (Correct)
....The satis ability problems in any of the classes CQMP and CMSP is NP complete. Remark 25 Another interesting question, related to the complexity result above, is the complexity of the satis ability problem in the class CPT of all frames W;R where R is just pseudo transitive. We know from [Ladner, 77] that the satis ability problem in the class CPT is PSPACE hard. However, there is no upper bound for this complexity problem, known to us. Since the satis ability problem in CPT is of rather technical than geometrical interest, we will not study it further. Now, we introduce the logic of ....
Ladner, R. The computational complexity of provability in systems of modal propositional logic. SIAM Journal of Computing, 6(1977), 467{ 480.
CardS4: Modal Theorem Proving on Java Smartcards - Goré, Nguyèn (Correct)
....j , then a is sure that it holds. We let the logically minded reader that the three formulae above and the necessitation rule all hold in any S4 model. 3.2. Proof Search in S4 Using Tableau Calculi The problem of deciding whether or not a formula is S4 satisfiable is known to be PSPACE complete [Lad77a, Lad77b]. The best known decision procedures use only O(n :logn) space [Hud] The most popular method for implementing theorem provers for S4 is to use the tableau method [Fit83, Gor99] This uses the rules of Figure 2, plus their duals for : and : obtained via the equivalences : j = j and : j = ....
....of the worlds in the current search branch. Thus checkList is always smaller than or equal to stack. Overall, the maximum number of configurations we might need to store in stack and checkList is of order n . Given that a configuration needs n bits, the space complexity of this algorithm is [Lad77a, Lad77b]. 4.6. An improved algorithm First, the non deterministic choice of the final part of the algorithm must be eliminated: some form of enumeration of formulae has to be implemented. For each formula j in currentWorld, we have to generate the initial configuration X j of a new world by just ....
R. Ladner. The computational complexity of provability in systems 6(3):467--480, 1977.
CardS4: Modal Theorem Proving on Java Smartcards - Goré, Nguyèn (Correct)
....j , then a is sure that it holds. We let the logically minded reader that the three formulae above and the necessitation rule all hold in any S4 model. 3.2. Proof Search in S4 Using Tableau Calculi The problem of deciding whether or not a formula is S4 satisfiable is known to be PSPACE complete [Lad77a, Lad77b]. The best known decision procedures use only O(n :logn) space [Hud] The most popular method for implementing theorem provers for S4 is to use the tableau method [Fit83, Gor99] This uses the rules of Figure 2, plus their duals for : and : obtained via the equivalences : j = j and : j = ....
....of the worlds in the current search branch. Thus checkList is always smaller than or equal to stack. Overall, the maximum number of configurations we might need to store in stack and checkList is of order n . Given that a configuration needs n bits, the space complexity of this algorithm is [Lad77a, Lad77b]. 4.6. An improved algorithm First, the non deterministic choice of the final part of the algorithm must be eliminated: some form of enumeration of formulae has to be implemented. For each formula j in currentWorld, we have to generate the initial configuration X j of a new world by just ....
R. Ladner. The computational complexity of provability in systems 6(3):467--480, September 1977.
A New Space Bound for the Modal Logics K4, KD4 and S4 - Nguyen (Correct)
....hitherto known for the considered logics. In particular space requirements for our logics are reduced from the previously established bound O(n : log n) to O(n: log n) 1 Introduction It is well known that complexity of provability for the modal logics K4, KD4 and S4 is PSPACE complete [5]. Recently, some authors have analyzed space requirements for modal logics [4, 10, 1, 8] In [4] Hudelmaier translates formulae to clausal form and proposes a contraction free sequent calculus, which is de ned only for clauses and has a decreasing measure for rules, for S4. Using the measure he ....
R. Ladner. The computational complexity of provability in systems of modal propositional logic. SIAM Journal of Computing, 6:467-480, 1977.
Optimizing a BDD-based Modal Solver - Pan, Vardi (Correct)
....connected with that of propositional satisfiability. In the past, a variety of approaches to propositional satisfiability have been combined with various approaches to handle modal connectives and implemented successfully. For example, a tableau based decision procedure for K is presented in [16, 12]. It is built on top of the propositional tableau construction procedure by forming a fully expanded propositional tableau and generating successor nodes on demand . A similar method uses the Davis Putnam Logemann Loveland (DPLL) method as the propositional engine by treating all modal ....
....With fixed density, depth, modal fraction, and number of atomic propositions, the complexity of the resulting formula can be varied by adjusting the density L=N . We used d = 1; 2, C = 3 and p = 0:5 in our experiments. A reduction of K to QBF Both K and QBF have PSPACE complete decision problems [16, 31]. This implies that the two problems are polynomially reducible to each other. A natural reduction from QBF to K is described in [12] In the last few years extensive effort was carried out into the development of highly optimized QBF solvers [17, 5] One motivation for this effort is the hope of ....
R.E. Ladner. The computational complexity of provability in systems of modal propositional logic. SIAM J. Comput., 6(3):467--480, 1977.
Combining Deduction and Model Checking into Tableaux and.. - De Giacomo, Massacci (1998) (8 citations) (Correct)
.... NEXPTIME tableaux into EXPTIME algorithms (x7) and conclude (x8) 2 Tableaux and Model Checking Techniques The use of tableaux for modal logics dates back to Kripke (see [13] for a recent overview or [11] for a classical treatment) and efficient procedures based on depth first search are known [14, 16]. Tableaux methods for satisfiability checking have been developed for the basic PDL [20, 22] but not for many extensions, such as CPDL, whereas automata theoretic techniques are available [26, 27] The problem is that PDLs, temporal logics or modal calculus cannot be tamed only by ....
R. Ladner. The computational complexity of provability in systems of modal propositional logic. SIAM J. of Computing, 6(3):467--480, Sept. 1977.
Deciding Regular Grammar Logics With Converse Through.. - Demri, de Nivelle (2003) (3 citations) (Correct)
....guarded fragment is possible thanks to the design of ecient resolutionbased decision procedures [Niv98,GdN99] In [Hla02] a tableau procedure for the guarded fragment with equality is implemented and tested. However, there are some simple modal logics with the satis ability problem in PSPACE ([Lad77]) that cannot be translated into GF using the relational translation. The reason for this is the fact that the frame condition that characterizes the logic cannot be expressed in GF: The simplest example of such a logic is probably S4 (many other examples will be given throughout the paper) ....
R. Ladner. The computational complexity of provability in systems of modal propositional logic. SIAM Journal of Computing, 6(3):467-480, September 1977.
BDD-Based Decision Procedures for K - Pan, Sattler, Vardi (2002) (10 citations) (Correct)
....connected with that of propositional satisfiability. In the past, a variety of approaches to propositional satisfiability have been combined with various approaches to handle modal connectives and implemented successfully. For example, a tableau based decision procedure for K is presented in [18, 14]. It is built on top of the propositional tableau construction procedure by forming a fully expanded propositional tableau and generating successor nodes on demand . A similar method uses the Davis Longemann Loveland method as the propositional engine by treating all modal subformulas as ....
R. E. Ladner. The computational complexity of provability in systems of modal propositional logic. SIAM J. Comput., 6(3):467--480, 1977.
Complexity Results for Logics of Local Reasoning and.. - Martin Allen Computer (Correct)
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Richard E. Ladner. The computational complexity of provability in systems of modal propositional logic. SIAM J. Computing, 6:467--480, 1977.
Complexity of Hybrid Logics over Transitive Frames - Mundhenk, Schneider.. (Correct)
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Ladner, R. E., The computational complexity of provability in systems of modal propositional logic, SIAM J. Comput. 6 (1977), pp. 467--480.
A Hierarchy of Modal Logics - Extended Version Thomas (Correct)
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R. E. Ladner. The computational complexity of provability in systems of modal propositional logic. SIAM Journal on Computing, 6 (3): 467--480, 1977.
The Complexity of the Disjunction and Existential Properties in .. - Buss, Mints (1999) (2 citations) (Correct)
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R. E. Ladner, The computational complexity of provability in systems of modal propositional logic, SIAM Journal on Computing, 6 (1977), pp. 467--480.
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R. Ladner. The computational complexity of provability in systems of modal logic. SIAM Journal on Computing, 6:467--480, 1977.
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R. Ladner. The computational complexity of provability in systems of modal logic. SIAM Journal on Computing, 6: pp. 467--480, 1977.
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R. Ladner. The computational complexity of provability in systems of modal logic. SIAM Journal on Computing, 6:467--480, 1977.
How Many Variables Does One Need to Prove PSPACE-hardness of .. - Chagrov, Rybakov (2003) (Correct)
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R. E. Ladner. The computational complexity of provability in systems of modal logic. SIAM Journal on Computing, 6:467-480, 1977.
Notes on the Space Requirements for Checking Satisfiability in.. - Kracht (2003) (2 citations) (Correct)
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R. E. Ladner. The computational complexity of provability in systems of modal logic. SIAM Journal of Computing, 6:467 - 480, 1977.
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R. Ladner. The computational complexity of provability in systems of modal propositional logic. SIAM journal of computing, 6(3):467--480, 1977.
The Random Modal QBF Test Set - Heguiabehere, de Rijke (2001) (Correct)
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R. Ladner. The computational complexity of provability in systems of modal logic. SIAM Journal on Computing, 6:467--480, 1977.
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R. Ladner. The computational complexity of provability in systems of modal logic. SIAM Journal on Computing, 6:467--480, 1977.
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R. Ladner. The computational complexity of provability in systems of modal propositional logic. SIAM Journal of Computing, 6, 467--480, 1977.
What is an Inference Rule? - Fagin, Halpern, Vardi (1992) (Correct)
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R. E. Ladner. The computational complexity of provability in systems of modal propositional logic. SIAM Journal on Computing, 6(3):467-480, 1977.
Products of Modal Logics, Part 1 - Dov Gabbay Department (Correct)
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R. Ladner. The computational complexity of provability in systems of modal logic. SIAM Journal on Computing, 6: pp. 467--480, 1977.
Decidable Fragments of First-Order and Fixed-Point Logic - From.. - Grädel (2003) (Correct)
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R. Ladner, The computational complexity of provability in systems of propositional modal logic, SIAM Journal on Computing, 6 (1977), pp. 467-480.
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