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651
Recognitionbycomponents: A theory of human image understanding
 Psychological Review
, 1987
"... The perceptual recognition of objects is conceptualized to be a process in which the image of the input is segmented at regions of deep concavity into an arrangement of simple geometric components, such as blocks, cylinders, wedges, and cones. The fundamental assumption of the proposed theory, recog ..."
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Cited by 1272 (23 self)
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The perceptual recognition of objects is conceptualized to be a process in which the image of the input is segmented at regions of deep concavity into an arrangement of simple geometric components, such as blocks, cylinders, wedges, and cones. The fundamental assumption of the proposed theory
MSO on the Infinite Binary Tree: Choice and Order
"... Abstract. We give a new proof showing that it is not possible to define in monadic secondorder logic (MSO) a choice function on the infinite binary tree. This result was first obtained by Gurevich and Shelah using set theoretical arguments. Our proof is much simpler and only uses basic tools from a ..."
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Cited by 10 (3 self)
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infinite binary tree with a wellfounded order has an undecidable MSOtheory. 1
On the decidability of MSO+U on infinite trees
"... Abstract. This paper is about mso+u, an extension of monadic secondorder logic, which has a quantifier that can express that a property of sets is true for arbitrarily large sets. We conjecture that the mso+u theory of the complete binary tree is undecidable. We prove a weaker statement: there is n ..."
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Abstract. This paper is about mso+u, an extension of monadic secondorder logic, which has a quantifier that can express that a property of sets is true for arbitrarily large sets. We conjecture that the mso+u theory of the complete binary tree is undecidable. We prove a weaker statement
Choice functions and wellorderings over the infinite binary tree
 Central European Journal of Mathematics
"... We give a new proof showing that it is not possible to define in monadic secondorder logic (MSO) a choice function on the infinite binary tree. This result was first obtained by Gurevich and Shelah using set theoretical arguments. Our proof is much simpler and only uses basic tools from automata th ..."
Trees, Grids, and MSO Decidability: from Graphs to Matroids
"... Monadic second order (MSO) logic proved to be a useful tool in many areas of application, reaching from decidability and complexity to picture processing, correctness of programs and parallel processes. To characterize the structural borderline between decidability and undecidability is a classical ..."
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Monadic second order (MSO) logic proved to be a useful tool in many areas of application, reaching from decidability and complexity to picture processing, correctness of programs and parallel processes. To characterize the structural borderline between decidability and undecidability is a classical
Undecidable FirstOrder Theories of Affine Geometries
, 2012
"... Tarski initiated a logicbased approach to formal geometry that studies firstorder structures with a ternary betweenness relation (β) and a quaternary equidistance relation (≡). Tarski established, inter alia, that the firstorder (FO) theory of (R 2, β, ≡) is decidable. Aiello and van Benthem (200 ..."
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of geometric structures (T, β), where T ⊆ Rn, and show that for each structure (T, β) ∈ C, the FOtheory of the class of monadic expansions of (T, β) is undecidable. We then consider classes of expansions of structures (T, β) with restricted unary predicates, for example finite predicates, and establish a
Realtime logics: complexity and expressiveness
 INFORMATION AND COMPUTATION
, 1993
"... The theory of the natural numbers with linear order and monadic predicates underlies propositional linear temporal logic. To study temporal logics that are suitable for reasoning about realtime systems, we combine this classical theory of in nite state sequences with a theory of discrete time, via ..."
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Cited by 252 (16 self)
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a monotonic function that maps every state to its time. The resulting theory of timed state sequences is shown to be decidable, albeit nonelementary, and its expressive power is characterized by! regular sets. Several more expressive variants are proved to be highly undecidable. This framework
The MSO Theory of Connectedly Communicating Processes
"... Abstract. We identify a network of sequential processes that communicate by synchronizing frequently on common actions. More precisely, we demand that there is a bound k such that if the process p executes k steps without hearing from process q—directly or indirectly—then it will neverhearfromq agai ..."
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Cited by 11 (0 self)
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again. The noninterleaved branching time behavior of a system of connectedly communicating processes (CCP) is given by its event structure unfolding. We show that the monadic second order (MSO) theory of the event structure unfolding of every CCP is decidable. Using this result, we also show
PVS: Combining Specification, Proof Checking, and Model Checking
, 1996
"... rem Proving and Typechecking The PVS specification language is based on classical, simply typed higherorder logic, but the type system has been augmented with subtypes and dependent types. Though typechecking is undecidable for the PVS type system, the PVS typechecker automatically checks for simp ..."
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Cited by 230 (5 self)
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rem Proving and Typechecking The PVS specification language is based on classical, simply typed higherorder logic, but the type system has been augmented with subtypes and dependent types. Though typechecking is undecidable for the PVS type system, the PVS typechecker automatically checks
The Limits of Decidability for First Order Logic on CPDA Graphs
 In STACS 2012, volume 14 of LIPIcs
, 2012
"... Higherorder pushdown automata (nPDA) are abstract machines equipped with a nested ‘stack of stacks of stacks’. Collapsible pushdown automata (nCPDA) extend these devices by adding ‘links ’ to the stack and are equiexpressive for tree generation with simply typed λY terms. Whilst the configuratio ..."
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Cited by 3 (0 self)
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the configuration graphs of HOPDA are well understood, relatively little is known about the CPDA graphs. The order2 CPDA graphs already have undecidable MSO theories but it was only recently shown by Kartzow [9] that firstorder logic is decidable at the second level. In this paper we show the surprising result
Results 1  10
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651