scholarly journals Combining the Delete Relaxation with Critical-Path Heuristics: A Direct Characterization

2016 ◽  
Vol 56 ◽  
pp. 269-327 ◽  
Author(s):  
Maximilian Fickert ◽  
Joerg Hoffmann ◽  
Marcel Steinmetz
Keyword(s):  
Recent Work ◽  
Polynomial Time ◽  
Critical Path ◽  
Complexity Reduction ◽  
Information Loss ◽  
The Other ◽  
Other Hand ◽  
Np Complete ◽  
Planning Task ◽  
The One

Recent work has shown how to improve delete relaxation heuristics by computing relaxed plans, i.e., the hFF heuristic, in a compiled planning task PiC which represents a given set C of fact conjunctions explicitly. While this compilation view of such partial delete relaxation is simple and elegant, its meaning with respect to the original planning task is opaque, and the size of PiC grows exponentially in |C|. We herein provide a direct characterization, without compilation, making explicit how the approach arises from a combination of the delete-relaxation with critical-path heuristics. Designing equations characterizing a novel view on h+ on the one hand, and a generalized version hC of hm on the other hand, we show that h+(PiC) can be characterized in terms of a combined hcplus equation. This naturally generalizes the standard delete-relaxation framework: understanding that framework as a relaxation over singleton facts as atomic subgoals, one can refine the relaxation by using the conjunctions C as atomic subgoals instead. Thanks to this explicit view, we identify the precise source of complexity in hFF(PiC), namely maximization of sets of supported atomic subgoals during relaxed plan extraction, which is easy for singleton-fact subgoals but is NP-complete in the general case. Approximating that problem greedily, we obtain a polynomial-time hCFF version of hFF(PiC), superseding the PiC compilation, and superseding the modified PiCce compilation which achieves the same complexity reduction but at an information loss. Experiments on IPC benchmarks show that these theoretical advantages can translate into empirical ones.

scholarly journals Complexity of Strong Approximation on the Sphere

2019 ◽  
Author(s):  
Naser T Sardari
Keyword(s):  
Polynomial Time ◽  
Strong Approximation ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
The Other ◽  
Ramanujan Graphs ◽  
Other Hand ◽  
Np Complete

Abstract By assuming some widely believed arithmetic conjectures, we show that the task of accepting a number that is representable as a sum of $d\geq 2$ squares subjected to given congruence conditions is NP-complete. On the other hand, we develop and implement a deterministic polynomial-time algorithm that represents a number as a sum of four squares with some restricted congruence conditions, by assuming a polynomial-time algorithm for factoring integers and Conjecture 1.1. As an application, we develop and implement a deterministic polynomial-time algorithm for navigating Lubotzky, Phillips, Sarnak (LPS) Ramanujan graphs, under the same assumptions.

scholarly journals Edge-Disjoint Branchings in Temporal Digraphs

2021 ◽  
Vol 28 (4) ◽  
Author(s):  
Victor Campos ◽  
Raul Lopes ◽  
Andrea Marino ◽  
Ana Silva
Keyword(s):  
Polynomial Time ◽  
Classical Result ◽  
The Other ◽  
Static Case ◽  
Edge Disjoint ◽  
Other Hand ◽  
Time Stamps ◽  
Np Complete

A temporal digraph ${\cal G}$ is a triple $(G, \gamma, \lambda)$ where $G$ is a digraph, $\gamma$ is a function on $V(G)$ that tells us the time stamps when a vertex is active, and $\lambda$ is a function on $E(G)$ that tells for each $uv\in E(G)$ when $u$ and $v$ are linked. Given a static digraph $G$, and a subset $R\subseteq V(G)$, a spanning branching with root $R$ is a subdigraph of $G$ that has exactly one path from $R$ to each $v\in V(G)$. In this paper, we consider the temporal version of Edmonds' classical result about the problem of finding $k$ edge-disjoint spanning branchings respectively rooted in given $R_1,\cdots,R_k$. We introduce and investigate different definitions of spanning branchings, and of edge-disjointness in the context of temporal digraphs. A branching ${\cal B}$ is vertex-spanning if the root is able to reach each vertex $v$ of $G$ at some time where $v$ is active, while it is temporal-spanning if each $v$ can be reached from the root at every time where $v$ is active. On the other hand, two branchings ${\cal B}_1$ and ${\cal B}_2$ are edge-disjoint if they do not use the same edge of $G$, and are temporal-edge-disjoint if they can use the same edge of $G$ but at different times. This lead us to four definitions of disjoint spanning branchings and we prove that, unlike the static case, only one of these can be computed in polynomial time, namely the temporal-edge-disjoint temporal-spanning branchings problem, while the other versions are $\mathsf{NP}$-complete, even under very strict assumptions. 

Decidability Questions for Insertion Systems and Related Models

2021 ◽  
Vol 180 (1-2) ◽  
pp. 53-76
Author(s):  
Andreas Malcher
Keyword(s):  
Polynomial Time ◽  
Regular Language ◽  
Regular Languages ◽  
The Other ◽  
Maximal Length ◽  
Membership Problem ◽  
Context Sensitive ◽  
Other Hand ◽  
Language Classes ◽  
The One

Insertion systems or insertion grammars are a generative formalism in which words can only be generated by starting with some axioms and by iteratively inserting strings subject to certain contexts of a fixed maximal length. It is known that languages generated by such systems are always context sensitive and that the corresponding language classes are incomparable with the regular languages. On the other hand, it is possible to generate non-semilinear languages with systems having contexts of length two. Here, we study decidability questions for insertion systems. On the one hand, it can be seen that emptiness and universality are decidable. Moreover, the fixed membership problem is solvable in deterministic polynomial time. On the other hand, the usually studied decidability questions such as, for example, finiteness, inclusion, equivalence, regularity, inclusion in a regular language, and inclusion of a regular language turn out to be undecidable. Interestingly, the latter undecidability results can be carried over to other models which are basically able to handle the mechanism of inserting strings depending on contexts. In particular, new undecidability results are obtained for pure grammars, restarting automata, clearing restarting automata, and forgetting automata.

Three theses concerning phonological representations

1974 ◽  
Vol 10 (1) ◽  
pp. 1-26 ◽  
Author(s):  
John Anderson ◽  
Charles Jones
Keyword(s):  
Recent Work ◽  
Syllable Structure ◽  
The Other ◽  
Structural Units ◽  
Phonological Representations ◽  
Other Hand ◽  
Per Se ◽  
The One

I. Some recent work in phonology/phonetics has tended to reaffirm the relevance of larger-than-segment (non-syntactico-morphological) structural units like the syllable: that is, that phonological representations are per se more highly structured than has generally been supposed in the immediate past. On the one hand, it has been argued that various ‘prosodic’ phenomena have as their domain non-arbitrary groupings of segments, including in particular groupings of ‘syllable size’ (e.g. Cheng, 1966; Lehiste, 1970), and that ‘morpheme structure conditions’ and redundancy conditions in general are most naturally interpreted as in large part constraints on syllable structure (cf., e.g., O'Connor & Trim, 1953; Fudge, 1969; Sampson, 1970; and the works they refer to). There have, on the other hand, been a number of studies particularly of co-articulation and of malfunctioning in production (stuttering, spoonerisms, etc.) whose import seems to be that ‘the unit of articulatory programming is larger in size than the segment, and makes it difficult to believe that articulation consists merely in the concatenation of phonemes’ (Kim, 1971: 60) - cf. the work surveyed by Kim and by Fromkin (1968).

scholarly journals Remarks on the Epistemic Interpretation of Paraconsistency Logic

2018 ◽  
Vol 22 (1) ◽  
pp. 153-170 ◽  
Author(s):  
Nicolás Lo Guercio ◽  
Damian Szmuc
Keyword(s):  
Recent Work ◽  
Paraconsistent Logic ◽  
Point Of View ◽  
The Other ◽  
Epistemic Rationality ◽  
Other Hand ◽  
Conflicting Evidence ◽  
Epistemic Interpretation ◽  
The One ◽  
The Way

In a recent work, Walter Carnielli and Abilio Rodrigues present an epistemically motivated interpretation of paraconsistent logic. In their view, when there is conflicting evidence with regard to a proposition A (i.e. when there is both evidence in favor of A and evidence in favor of ￢A) both A and ￢A should be accepted without thereby accepting any proposition B whatsoever. Hence, reasoning within their system intends to mirror, and thus, should be constrained by, the way in which we reason about evidence. In this article we will thoroughly discuss their position and suggest some ways in which this project can be further developed. The aim of the paper is twofold. On the one hand, we will present some philosophical critiques to the specific epistemic interpretation of paraconsistent logic proposed by Carnielli & Rodrigues. First, we will contend that Carnielli & Rodrigues’s interpretation implies a thesis about what evidence rationally justifies to accept or believe, called Extreme Permissivism, which is controversial among epistemologists. Second, we will argue that what agents should do, from an epistemic point of view, when faced with conflicting evidence, is to suspend judgment. On the other hand, despite these criticisms we do not believe that the epistemological motivation put forward by Carnielli & Rodrigues is entirely wrong. In the last section, we offer an alternative way in which one might account for the epistemic rationality of accepting contradictions and, thus, for an epistemic understanding of paraconsistency, which leads us to discuss the notion of diachronic epistemic rationality.

English prepositions: A stratificational approach

1968 ◽  
Vol 4 (2) ◽  
pp. 153-172 ◽  
Author(s):  
David C. Bennett
Keyword(s):  
Recent Work ◽  
The Other ◽  
International Congress ◽  
Clear Picture ◽  
General Shape ◽  
Componential Analysis ◽  
Other Hand ◽  
Theory Of Language ◽  
The One ◽  
The Relationship

In a paper read at the Tenth International Congress of Linguists, Bucharest, 1967 (Bennett, forthcoming), I discussed the question of synonymy within the framework of the stratificational theory of language, taking examples from the area of English prepositions. The present paper has two aims. On the one hand, it incorporates the findings of more recent work on synonymy. Thus whereas, for instance, in the earlier paper two levels of synonymy were distinguished, it now seems necessary to recognize four or possibly five levels. On the other hand, the paper will attempt to set the discussion of synonymy in a wider framework by sketching the outlines of a semological description of English prepositions. To present such a description would be beyond the scope of the paper. I hope merely to indicate the general shape that the description might take. In addition to the remarks on synonymy there will be some discussion of polysemy, componential analysis and idioms. In particular it is hoped that a clear picture will emerge of the relationship between these various areas.

Extending the Domain of Care in Philippe Forest

2020 ◽  
Vol 57 (3) ◽  
pp. 352-364
Author(s):  
ANNA MAGDALENA ELSNER
Keyword(s):  
Medical Care ◽  
Recent Work ◽  
Ethics Of Care ◽  
The Other ◽  
Medical Setting ◽  
Other Hand ◽  
The Dead ◽  
The One ◽  
Taking Care

This article explores the connection between care and loss in Philippe Forest’s work by drawing on the etymological origins of care and on contemporary French writing on the ethics of care. On the one hand, care in Forest comes to stand for the technical taking care of a patient in the medical setting as well as for caring for and about his dying child specifically. On the other hand, the practice of writing about the loss of his daughter turns into a form of long-term caring for both his dead daughter and her surviving father. This continued attention to a relationship built around loss is, according to Forest, missing in practices of medical care supposedly meant to acknowledge death. The article argues that engaging with loss is key to the practice of care, even if, as Forest’s more recent work shows, this engagement also entails documenting a gradual forgetting of the dead.

Just Nationalism: The Future of an Illusion

1996 ◽  
Vol 22 ◽  
pp. 345-363
Author(s):  
Andrew Levine
Keyword(s):  
Political Philosophy ◽  
Recent Work ◽  
Theory And Practice ◽  
The Other ◽  
The Past ◽  
Other Hand ◽  
The World ◽  
The Future ◽  
The Face ◽  
The One

Until quite recently, political philosophers routinely ignored nationalism. Nowadays, the topic is very much on the philosophical agenda. In the past, when philosophers did discuss nationalism, it was usually to denigrate it. Today, nationalism elicits generally favorable treatment. I confess to a deep ambivalence about this turn of events. On the one hand, much of what has emerged in recent work on nationalism appears to be on the mark. On the other hand, the anti- or extra-nationalist outlook that used to pervade political philosophy seems as sound today as it ever was, and perhaps even more urgent in the face of truly horrendous eruptions of nationalist hostilities in many parts of the world. What follows is an effort to grapple with this ambivalence. My aim will be to identify what is defensible in the nationalist idea and then to reflect on the flaws inherent in even the most defensible aspects of nationalist theory and practice.

scholarly journals Shifts with decidable language and non-computable entropy

2008 ◽  
Vol Vol. 10 no. 3 (Automata, Logic and Semantics) ◽  
Author(s):  
Peter Hertling ◽  
Christoph Spandl
Keyword(s):  
Real Number ◽  
Topological Entropy ◽  
Polynomial Time ◽  
The Other ◽  
Other Hand ◽  
Enumerable Language ◽  
International Audience ◽  
Full Shift ◽  
The One ◽  
Infinite Sequences

Automata, Logic and Semantics International audience We consider subshifts of the full shift of all binary bi-infinite sequences. On the one hand, the topological entropy of any subshift with computably co-enumerable language is a right-computable real number between 0 and 1. We show that, on the other hand, any right-computable real number between 0 and 1, whether computable or not, is the entropy of some subshift with even polynomial time decidable language. In addition, we show that computability of the entropy of a subshift does not imply any kind of computability of the language of the subshift

Stories and the Self

2020 ◽  
Vol 32 (2) ◽  
pp. 47-58 ◽  
Author(s):  
Stefan Krause ◽  
Markus Appel
Keyword(s):  
Meta Analysis ◽  
The Self ◽  
The Other ◽  
Lower Degree ◽  
Contrast Effects ◽  
Self Perception ◽  
Self Perceptions ◽  
Other Hand ◽  
The One ◽  
Implicit And Explicit

Abstract. Two experiments examined the influence of stories on recipients’ self-perceptions. Extending prior theory and research, our focus was on assimilation effects (i.e., changes in self-perception in line with a protagonist’s traits) as well as on contrast effects (i.e., changes in self-perception in contrast to a protagonist’s traits). In Experiment 1 ( N = 113), implicit and explicit conscientiousness were assessed after participants read a story about either a diligent or a negligent student. Moderation analyses showed that highly transported participants and participants with lower counterarguing scores assimilate the depicted traits of a story protagonist, as indicated by explicit, self-reported conscientiousness ratings. Participants, who were more critical toward a story (i.e., higher counterarguing) and with a lower degree of transportation, showed contrast effects. In Experiment 2 ( N = 103), we manipulated transportation and counterarguing, but we could not identify an effect on participants’ self-ascribed level of conscientiousness. A mini meta-analysis across both experiments revealed significant positive overall associations between transportation and counterarguing on the one hand and story-consistent self-reported conscientiousness on the other hand.

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