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NP-Logic Systems and Model-Equivalence Reductions

Yuping Shen, Xishun Zhao
2010 Electronic Proceedings in Theoretical Computer Science  
In this paper we investigate the existence of model-equivalence reduction between NP-logic systems which are logic systems with model existence problem in NP.  ...  It is shown that among all NP-systems with model checking problem in NP, the existentially quantified propositional logic (\exists PF) is maximal with respect to poly-time model-equivalent reduction.  ...  Conclusion and Future work We have proved that w.r.t. poly-time model-equivalent reduction (∃PF, TA, FSat) has the strongest expressive power among NP systems with model checking problem in NP, whereas  ... 
doi:10.4204/eptcs.24.17 fatcat:7gnhhnrkavft7nssbv2yi266ja

Page 20 of Mathematical Reviews Vol. , Issue 85a [page]

1985 Mathematical Reviews  
The author observes that the set SAT @ SAT is NP-equivalent (its intractability can be shown by a reduction from an NP-complete set to it) and shows that, assuming NP¥co-NP, there exist sets in AP —(NPUco-NP  ...  ) which are not NP-equivalent.  ... 

On Slicewise Monotone Parameterized Problems and Optimal Proof Systems for TAUT [chapter]

Yijia Chen, Jörg Flum
2010 Lecture Notes in Computer Science  
For a reasonable sound and complete proof calculus for first-order logic consider the problem to decide, given a sentence ϕ of first-order logic and a natural number n, whether ϕ has no proof of length  ...  This equivalence is an instance of a general result linking the complexity of so-called slicewise monotone parameterized problems with the existence of an optimal proof system for TAUT.  ...  This research has been partially supported by the National Nature Science Foundation of China (60970011), the Sino-German Center for Research Promotion (GZ400), and the John Templeton Foundation through  ... 
doi:10.1007/978-3-642-15205-4_18 fatcat:4ge5ewg3graapmfn7fdqtvb5za

Page 511 of Mathematical Reviews Vol. , Issue 99a [page]

1991 Mathematical Reviews  
These systems include the classical formulation of NP, interactive proof systems, computationally sound proof systems, and prob- abilistically checkable proofs, which are closely related to multi- prover  ...  It turns out that many questions in computational complexity, in particular, the complexity the- ory for small-depth families of Boolean circuits, are equivalent to expressibility questions in finite model  ... 

Page 3995 of Mathematical Reviews Vol. , Issue 83j [page]

1983 Mathematical Reviews  
In this paper, we give hack-and-forth systems characterizing elementary equivalence in those logics and their fragments of bounded quantifier rank. This generalizes work of R. Fraissé and A.  ...  every model elementarily equivalent to (w, +,0,1,<).  ... 

The complexity of model checking for propositional default logics

Paolo Liberatore, Marco Schaerf
2005 Data & Knowledge Engineering  
In this paper we analyze the complexity of deciding whether a propositional interpretation is a model of a default theory for some of the variants of default logic presented in the literature.  ...  Default logic is one of the most widely used formalisms to formalize commonsense reasoning.  ...  Since these are n defaults, this is a reduction from the problem of the minimal model to model checking of default logics.  ... 
doi:10.1016/j.datak.2005.03.002 fatcat:iyd7vci7njeytdxyvaboulzogq

Page 2583 of Mathematical Reviews Vol. , Issue 96e [page]

1996 Mathematical Reviews  
Moreover, the notion can be easily extended to other reduction systems such as Girard’s second-order system F and Gédel’s system T.  ...  ), and the leftmost reduction theorem for y-reduction.” 96e:03018 03B45 van Benthem, Johan (NL-AMST-LL; Amsterdam) Beyond accessibility: functional models for modal logic.  ... 

Page 482 of Mathematical Reviews Vol. , Issue 98A [page]

1998 Mathematical Reviews  
We define the least stringent of these models (*“FDAS’), and put it in context with other models defined in the literature.  ...  This tight, three-way relationship among fix- point logics, relational complexity and standard complexity yields in a uniform way logical analogues to all containments among the complexity classes P, NP  ... 

Page 620 of Mathematical Reviews Vol. , Issue 96b [page]

1996 Mathematical Reviews  
It was also shown that formulas of Carnap’s logic are structurally equivalent to trees of NP queries, more precisely, of satisfiability tests. In this paper, we give a survey of these results.  ...  Recently, it turned out that there are interesting connections between Carnap’s modal logic and finite model theory for modal logics.  ... 

Page 44 of Mathematical Reviews Vol. , Issue 97A [page]

1997 Mathematical Reviews  
Scott (3-OTTW; Ottawa, ON) 03 MATHEMATICAL LOGIC AND FOUNDATIONS 97a:03064 03F05 68Q42 Kumeta, Akefumi Extracting a reduction system from a conjunction calculus.  ...  Indeed, in work with Asperti and Laneve, they showed the equivalence of several notions of “reduction” paths in lambda calculus (e.g.  ... 

Page 3589 of Mathematical Reviews Vol. , Issue 90F [page]

1990 Mathematical Reviews  
System Sci. 36 (1988), no. 3, 336-350. Summary: “All sets complete for NP under 1-L reductions are complete under length-increasing, invertible, and ‘almost one-to- one’ <?, reductions.  ...  The operational semantics make use of Hennessy’s and Plotkin’s transition systems. All models are built on metric structures, and involve continuations in an essen- tial way.  ... 

Characterising equilibrium logic and nested logic programs: Reductions and complexity,

DAVID PEARCE, HANS TOMPITS, STEFAN WOLTRAN
2009 Theory and Practice of Logic Programming  
AbstractEquilibrium logic is an approach to non-monotonic reasoning that extends the stable-model and answer-set semantics for logic programs.  ...  We provide reductions not only for decision problems, but also for the central semantical concepts of equilibrium logic and nested logic programs.  ...  A reduction approach to disjunctive logic programs is also realised by several systems for equivalence checking.  ... 
doi:10.1017/s147106840999010x fatcat:4qwun6nfb5ctdpxdmnnulw5nmu

Computation Tree Logic for Synchronization Properties [article]

Krishnendu Chatterjee, Laurent Doyen
2016 arXiv   pre-print
We show that our variant of CTL is decidable and that the model-checking problem is in Delta_3^P = P^NP^NP, and is DP-hard.  ...  The distinguishing power of CTL and of our new logic coincide if the Next operator is allowed in the logics, thus the classical bisimulation quotient can be used for state-space reduction before model  ...  We thank Stefan Göller and anonymous reviewers for their insightful comments and suggestions.  ... 
arXiv:1604.06384v2 fatcat:xzrrpqbtbne5ndinyz7xn7tq6i

On the Computational Complexity of Verifying One-Counter Processes

Stefan Goller, Richard Mayr, Anthony Widjaja To
2009 2009 24th Annual IEEE Symposium on Logic In Computer Science  
We study the complexity of two closely related verification problems over one-counter processes: model checking with the temporal logic EF, where formulas are given as directed acyclic graphs, and weak  ...  We also show that there already exists a fixed EF formula (resp. a fixed finite system) such that model checking (resp. weak bisimulation) over one-counter processes is hard for P NP [log] .  ...  ACKNOWLEDGMENT We thank Dietrich Kuske, Leonid Libkin, Markus Lohrey, and Christian Mathissen for their comments.  ... 
doi:10.1109/lics.2009.37 dblp:conf/lics/GollerMT09 fatcat:lbjn7wfqj5ahtj4jydadq3wbge

Page 2294 of Mathematical Reviews Vol. , Issue 86f [page]

1986 Mathematical Reviews  
A class M of finite models in L is MATHEMATICAL LOGIC AND FOUNDATIONS 2294 interpretive NP-complete (abbreviated as INP) if M € NP and for every class M’ € NP of finite L’-models which is closed under  ...  Dahlhaus, Elias (D-TUB) 86f:03060 Reduction to NP-complete problems by interpretations. Logic and machines: decision problems and complezity (Minster, 1983), 357-365, Lecture Notes in Comput.  ... 
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