scholarly journals The Power of Counting Logics on Restricted Classes of Finite Structures

2007 ◽  
pp. 84-98 ◽  
Author(s):  
Anuj Dawar ◽  
David Richerby
Keyword(s):  
Finite Structures

Logical Decision Problems and Complexity of Logic Programs

1987 ◽  
Vol 10 (1) ◽  
pp. 1-33
Author(s):  
Egon Börger ◽  
Ulrich Löwen
Keyword(s):  
Fixed Point ◽  
Computational Complexity ◽  
Decision Problem ◽  
Decision Problems ◽  
Complexity Classes ◽  
Logic Programs ◽  
Finite Structures ◽  
Syntactic Restrictions

We survey and give new results on logical characterizations of complexity classes in terms of the computational complexity of decision problems of various classes of logical formulas. There are two main approaches to obtain such results: The first approach yields logical descriptions of complexity classes by semantic restrictions (to e.g. finite structures) together with syntactic enrichment of logic by new expressive means (like e.g. fixed point operators). The second approach characterizes complexity classes by (the decision problem of) classes of formulas determined by purely syntactic restrictions on the formation of formulas.

scholarly journals Finite representability of semigroups with demonic refinement

2021 ◽  
Vol 82 (2) ◽  
Author(s):  
Robin Hirsch ◽  
Jaš Šemrl
Keyword(s):  
Partial Order ◽  
Turing Machines ◽  
Binary Relations ◽  
Finite Representation ◽  
First Order ◽  
Finite Structures ◽  
Finite Base ◽  
Finite Set ◽  
Finite Representability ◽  
Representation Class

AbstractThe motivation for using demonic calculus for binary relations stems from the behaviour of demonic turing machines, when modelled relationally. Relational composition (; ) models sequential runs of two programs and demonic refinement ($$\sqsubseteq $$ ⊑ ) arises from the partial order given by modeling demonic choice ($$\sqcup $$ ⊔ ) of programs (see below for the formal relational definitions). We prove that the class $$R(\sqsubseteq , ;)$$ R ( ⊑ , ; ) of abstract $$(\le , \circ )$$ ( ≤ , ∘ ) structures isomorphic to a set of binary relations ordered by demonic refinement with composition cannot be axiomatised by any finite set of first-order $$(\le , \circ )$$ ( ≤ , ∘ ) formulas. We provide a fairly simple, infinite, recursive axiomatisation that defines $$R(\sqsubseteq , ;)$$ R ( ⊑ , ; ) . We prove that a finite representable $$(\le , \circ )$$ ( ≤ , ∘ ) structure has a representation over a finite base. This appears to be the first example of a signature for binary relations with composition where the representation class is non-finitely axiomatisable, but where the finite representation property holds for finite structures.

Time and Duration in Noninterleaving Concurrency

1993 ◽  
Vol 19 (3-4) ◽  
pp. 403-416
Author(s):  
David Murphy
Keyword(s):  
Partial Order ◽  
Independent Interest ◽  
Underlying Event ◽  
Strict Partial Order ◽  
Event Structures ◽  
Concurrency Theory ◽  
Finite Structures

The purpose of this paper is to present a real-timed concurrency theory in the noninterleaving tradition. The theory is based on the occurrences of actions; each occurrence or event has a start and a finish. Causality is modelled by assigning a strict partial order to these starts and finishes, while timing is modelled by giving them reals. The theory is presented in some detail. All of the traditional notions found in concurrency theories (such as conflict, confusion, liveness, and so on) are found to be expressible. Four notions of causality arise naturally from the model, leading to notions of securing. Three of the notions give rise to underlying event structures, demonstrating that our model generalises Winskel’s. Infinite structures are then analysed: a poset of finite structures is defined and suitably completed to give one containing infinite structures. These infinite structures are characterised as just those arising as limits of finite ones. Our technique here, which relies on the structure of time, is of independent interest.

ESTIMATION OF VIBRATION DISTRIBUTION FOR FINITE STRUCTURES

2000 ◽  
Vol 238 (2) ◽  
pp. 271-293 ◽  
Author(s):  
J. LIANG ◽  
B.A.T. PETERSSON
Keyword(s):  
Finite Structures

scholarly journals THE THEORY OF SPECTRUM EXCHANGEABILITY

2014 ◽  
Vol 8 (1) ◽  
pp. 108-130
Author(s):  
E. HOWARTH ◽  
J. B. PARIS
Keyword(s):  
Probability Function ◽  
Inductive Logic ◽  
Probability Functions ◽  
Homogeneous Functions ◽  
Finite Structures ◽  
Spectrum Exchangeability

AbstractSpectrum Exchangeability, Sx, is an irrelevance principle of Pure Inductive Logic, and arguably the most natural (but not the only) extension of Atom Exchangeability to polyadic languages. It has been shown1 that all probability functions which satisfy Sx are comprised of a mixture of two essential types of probability functions; heterogeneous and homogeneous functions. We determine the theory of Spectrum Exchangeability, which for a fixed language L is the set of sentences of L which must be assigned probability 1 by every probability function satisfying Sx, by examining separately the theories of heterogeneity and homogeneity. We find that the theory of Sx is equal to the theory of finite structures, i.e., those sentences true in all finite structures for L, and it emerges that Sx is inconsistent with the principle of Super-Regularity (Universal Certainty). As a further consequence we are able to characterize those probability functions which satisfy Sx and the Finite Values Property.

Vibration Response and Wave Propagation in Periodic Structures

1971 ◽  
Vol 93 (3) ◽  
pp. 783-792 ◽  
Author(s):  
Denys J. Mead
Keyword(s):  
Periodic Structures ◽  
Vibration Response ◽  
Flexural Wave ◽  
Wave Groups ◽  
Pressure Fields ◽  
Finite Structures ◽  
Modal Density ◽  
Flexible Supports ◽  
Physical Insight ◽  
Structural Configurations

The vibration response of periodic, beam-like structures has conventionally been studied either by transfer matrix or normal mode methods. The latter method becomes unwieldy if the damping and modal density are high, whereas the former method does not lend itself readily to giving physical understanding. It is shown in this paper that a special class of flexural wave groups can exist in periodic structures; an understanding of them permits a ready formulation of the response-calculation problem. The formulation can be applied to both infinite and finite structures, and the amount of damping present may have any value. The method is specially well adapted to studying response due to convected pressure fields and loadings and gives great physical insight. Illustrations are given relating to beams resting at regular intervals on flexible supports and to aeronautical rib-skin structures. Some calculated values of vibration response are presented and discussed and optimum structural configurations are considered.

scholarly journals Syntactic categories informing variationist analysis: The case of English copy-raising

2015 ◽  
Author(s):  
Marisa Alana Brook
Keyword(s):  
Large City ◽  
Trade Off ◽  
Finite Structures ◽  
Syntactic Properties ◽  
Copy Raising ◽  
As If ◽  
Subject Raising

<p>This paper re-examines variation between the comparative complementizers (AS IF, AS THOUGH, LIKE, THAT, and Ø) that follow verbs denoting ostensibility (SEEM, APPEAR, LOOK, SOUND, and FEEL) in the large city of Toronto, Canada. Given that younger speakers appear to be using more of these structures in the first place, I evaluate the hypothesis that there is a trade-off in apparent time between these finite structures and the non-finite construction of Subject-to-Subject raising. Focusing on the verb SEEM, I find that the non-finite structures are losing ground in apparent time to the finite ones. I subsequently address the issue of how best to divide up the finite tokens as co-variants opposite the finite constructions, and find that a split according to syntactic properties – whether or not the copy-raising transformation is permitted – tidily accounts for the patterning and reveals a straightforward change in progress. The results reaffirm the value of using variationist methodology to test competing claims, and also establish that variation can behave in a classic way even among whole syntactic categories.</p>

Forcing in Finite Structures

1997 ◽  
Vol 43 (3) ◽  
pp. 401-412 ◽  
Author(s):  
Domenico Zambella
Keyword(s):  
Finite Structures
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