Trivial Composition Research Articles

Toward the Emergence of Nontrivial Compositionality

All natural languages exhibit a distinction between content words (nouns, verbs, etc.) and function words (determiners, auxiliaries, tenses, etc.). Yet surprisingly little has been said about the emergence of this universal architectural feature of human language. This article argues that the existence of this distinction requires the presence of nontrivial compositionality and identifies assumptions that have previously been made in the literature that provably guarantee only trivial composition. It then presents a signaling game with variable contexts and shows how the distinction can emerge via reinforcement learning.

Hardware Private Circuits: From Trivial Composition to Full Verification

The design of glitch-resistant higher-order masking schemes is an important challenge in cryptographic engineering. A recent work by Moos <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> (CHES 2019) showed that most published schemes (and all efficient ones) exhibit local or composability flaws at high security orders, leaving a critical gap in the literature on hardware masking. In this article, we first extend the simulatability framework of Belaïd <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> (EUROCRYPT 2016) and prove that a compositional strategy that is correct without glitches remains valid with glitches. We then use this extended framework to prove the first masked gadgets that enable trivial composition with glitches at arbitrary orders. We show that the resulting “Hardware Private Circuits” approach the implementation efficiency of previous (flawed) schemes. We finally investigate how trivial composition can serve as a basis for a tool that allows verifying full masked hardware implementations (e.g., of complete block ciphers) at any security order from their HDL code. As side products, we improve the randomness complexity of the best published refreshing gadgets, show that some S-box representations allow latency reductions and confirm practical claims based on implementation results.

Trivially and Efficiently Composing Masked Gadgets With Probe Isolating Non-Interference

We revisit the analysis and design of masked cryptographic implementations to prevent side-channel attacks. Our starting point is the (known) observation that proving the security of a higher-order masked block cipher exhaustively requires unrealistic computing power. As a result, a natural strategy is to split algorithms in smaller parts (or gadgets), with as main objectives to enable both simple composition (as initiated by Barthe et al. at CCS 2016) and efficient implementations. We argue that existing composition strategies allow either trivial composition with significant overheads or optimized composition with more analysis efforts. As a result, we first introduce a new definition of Probe Isolating Non-Interference (PINI) that allows both trivial composition and efficient implementations. We next prove general composition theorems for PINI gadgets that considerably simplify the analysis of complex masked implementations. We finally design efficient multiplication gadgets that satisfy this definition. As additional results, we exhibit a limitation of existing compositional strategies for the analysis of Multiple-Inputs / Multiple-Outputs (MIMO) gadgets, extend Barthe et al. definition of Strong Non-Interference (SNI) to deal with this context, and describe an optimization method to design efficient MIMO-SNI (sub)circuits. Our results allow proving the security of a recent masked AES implementation by Goudarzi and Rivain (EUROCRYPT 2017). From the implementation viewpoint, PINI implementations reach the level of performance of the best composable masking schemes for the AES Rijndael, and outperform them by significant factors for lightweight ciphers.

Structured propositions and trivial composition

Structured propositions are often invoked to explain why intensionally equivalent sentences do not substitute salva veritate into attitude ascriptions. As the semantics is standardly developed—for example, in Salmon (Frege’s puzzle. Ridgeview, Atascadero, CA, 1986), Soames (Philos Top 15(1):47–87, 1987) and King (Noûs 29(4):516–535, 1995), the semantic value of a complex expression is an ordered complex consisting of the semantic values of its components. Such views, however, trivialize semantic composition since they do not allow for independent constraints on the meaning of complexes. Trivializing semantic composition risks “trivializing semantics” (King and Stanley, in: Szabó (ed) Semantics versus pragmatics, Oxford University Press, Oxford, 2005). Yet, proponents of structured propositions suggest a route to reimpose substantive compositionality. While the mapping from a sentence to the structured proposition it expresses is trivially compositional, there is a non-trivial mapping from the structured proposition to its truth-value. This non-trivial level of semantic composition allows the meanings assigned to complex expressions to impose substantive constraints on the meanings of the simple ones. I first articulate the basic desiderata: an account of structured propositions capable of explaining attitude attributions and of delivering a non-trivially compositional semantics. I then show that the two-stage semantics proposed by standard proponents of structured propositions does not satisfy these joint goals.

The problem of counterfactual de re attitudes

The problem of counterfactual attitudes de re was identified by Ninan (2008) as a challenge for standard theories of de re. I show that once counterfactual non-de re attitudes are properly analyzed, trivial composition of such an analysis for them with the analysis of doxastic de re provides the solution to the problem. Thus there is no independent phenomenon of counterfactual attitudes de re, and therefore no problem as such.

The problem of counterfactual de re attitudes

The problem of counterfactual attitudes de re was identified by Ninan (2008) as a challenge for standard theories of de re. I show that once counterfactual non-de re attitudes are properly analyzed, trivial composition of such an analysis for them with the analysis of doxastic de re provides the solution to the problem. Thus there is no independent phenomenon of counterfactual attitudes de re, and therefore no problem as such.

Average dimension of fixed point spaces with applications

Let G be a finite group, F a field, and V a finite dimensional FG-module such that G has no trivial composition factor on V. Then the arithmetic average dimension of the fixed point spaces of elements of G on V is at most (1/p)dimV where p is the smallest prime divisor of the order of G. This answers and generalizes a 1966 conjecture of Neumann which also appeared in a paper of Neumann and Vaughan-Lee and also as a problem in The Kourovka Notebook posted by Vaughan-Lee. Our result also generalizes a recent theorem of Isaacs, Keller, Meierfrankenfeld, and Moretó. We also classify precisely when equality can occur. Various applications are given. For example, another conjecture of Neumann and Vaughan-Lee is proven and some results of Segal and Shalev are improved and/or generalized concerning BFC groups.

Across the Great Divide: Anxieties of Acculturation in College English

/ hear complaints about trivial composition research spoken by scholars whose whole lives have been spent discovering and teaching trivia. I hear complaints about dry-as-dust literary scholar ship spoken by composition teachers who never read anything if its not in a freshman textbook and whose accounts of what they teach and how they appraise it are parodies of dry pedantry. Only those who fraternize in the no-man's-land between the two camps discover how badly the two sides need each other.

Elementary Divisors of Gram Matrices of Certain Specht Modules

The elementary divisors of the Gram matrices of Specht modules S λ over the symmetric group are determined for two-row partitions and for two-column partitions λ. More precisely,the subquotients of the Jantzen filtration are calculated using Schaper's formula. Moreover,considering a general partition λ of n at a prime p > n − λ1,the only possible non trivial composition factor of is induced by the morphism of Carter and Payne,as shown by means of Kleshchev's modular branching rule. This enables the Jantzen filtration to be calculated in this case as well.

The number of trivial composition factors of the Steinberg module

The number of trivial composition factors of the Steinberg module

The Tomocerinae (Collembola) in Old Field Stands of North Carolina

An investigation of the Tomocerinae was concducted in a selected series of old field successional .stands in the Piedmont of North Carolina to determine the variability in size and trivial composition of populations in different seral stages of old field communities. An analysis of seasonal fluctuations in density and frequency of the several species was computed to decide what microclimatic factors affected each member of the .subfamily; stratal sampling was employed to establish the possibility of vertical migrations in the litter-humus layer and underlying soil strata. The Piedmont region of North Carolina presents an orderly secondary succession of vegetation following the abandonment of upland fields (Oosting 1942). Five types of old field communities were chosen for study with paired stations established for each successional stage with most stations located in the Duke University Forest (Figure 1). The author is grateful to Dr. I. E. Gray of the Department of Zoology, -Duke University, for guidance and helpful criticisms, anid to Dr. David Wray of the North Carolina Department of Agriculture for confirming the -identifications of the Tomocerinae.