Weighted Pushdown Systems with Indexed Weight Domains

The reachability analysis of weighted pushdown systems is a very powerful technique in verification and analysis of recursive programs. Each transition rule of a weighted pushdown system is associated with an element of a bounded semiring representing the weight of the rule. However, we have realized that the restriction of the boundedness is too strict and the formulation of weighted pushdown systems is not general enough for some applications. To generalize weighted pushdown systems, we first introduce the notion of stack signatures that summarize the effect of a computation of a pushdown system and formulate pushdown systems as automata over the monoid of stack signatures. We then generalize weighted pushdown systems by introducing semirings indexed by the monoid and weaken the boundedness to local boundedness

Deterring Nuclear Attacks on Japan: An Examination of the U.S.-Japan Relationship and Nuclear Modernization

This paper evaluates the effectiveness of the U.S. nuclear weapons arsenal in covering security commitments with its foreign allies, particularly Japan. The U.S. has promised to defend allies all over the world with nuclear forces, and consequently has been forced into a delicate and precarious position. President Barack Obama wants to reach nuclear zero, which would make the world safe from nuclear destruction in the future; yet he also wants to provide security for allied nations in the present, using the very weapons he has marked for destruction. And he is facing an aging Cold War-era nuclear arsenal that needs serious repairs and upgrades in order to remain a credible and capable deterrent. This paper argues that while the U.S nuclear posture up to this point has been satisfactory enough to prevent panic and ensure protection of Japan, the evolving nuclear posture from this point onward will strengthen the credibility of existing security commitments, deter potential attackers, and give Japan the confidence to become a more coordinated partner in the relationship. Components of the paper include the evolution of U.S. nuclear strategy and deterrence, the three historical occurrences of tensions between the U.S. and Japan over nuclear issues, and the current concerns and actions in the alliance today

Trends and Implications: The Use of Facebook in the Professional World

The recent trend of connectivity through the Internet has served as a spark for the social media era, resulting in a number of social websites such as Xanga (social blogging site),MySpace, Facebook, Twitter, LinkedIn, and many others. Facebook specifically has become an everyday norm in the lives of most young adults. With the societal shift towards a digitally orientated lifestyle, there is an increased interaction between friends, family, and non-acquaintances via social networking sites like Facebook. As a result, the manner in which users portray themselves online becomes influential for new friends viewing their pages. Similarly, professional companies are now utilizing Facebook for marketing, promotions, and even recruiting. This becomes an issue, then, for young adults looking to launch their careers and are unaware of the way in which companies utilize Facebook. The purpose of this study was to identify how companies use Facebook and whether or not there is a “knowledge gap” between young adults and professionals. Upon learning if and how companies use Facebook, young adults can be informed on how to present themselves online so as to balance their social and professional online image. The results of the study identified a shifting trend towards companies using Facebook in the near future; as social networking merges together with professional networking, it becomes increasingly important to adopt a long-termed mindset. Cautionary tactics are recommended, such as adjusting privacy settings and removing inappropriate images

Anabelian Geometry for Henselian Discrete Valuation Fields with Quasi-finite Residues

Let p, l be prime numbers. In anabelian geometry for p-adic local fields [i.e., finite extension fields of the field of p-adic numbers], many topics have been discussed. In the present paper, we generalize two of the topics --discovered by S. Mochizuki-- to more general complete discrete valuation fields. One is the mono-anabelian reconstruction, under a certain indeterminacy, of the cyclotomic rigidity isomorphism between the usual cyclotome Ẑ(1) associated to a p-adic local field and the cyclotome constructed, in a purely group-theoretic way, from [the underlying topological group structure of] the absolute Galois group of the p-adic local field. The other is the Neukirch-Uchida-type result, i.e., the field-theoreticity of an outer isomorphism between the absolute Galois groups of p-adic local fields that preserves the respective ramification filtrations. For our generalizations, we first discuss l-local class field theory for Henselian discrete valuation fields with strongly l-quasi-finite residue fields [i.e., perfect fields such that the maximal pro-l quotients of the absolute Galois groups of their finite extension fields are isomorphic to Ẑl] of characteristic p via Artin-Tate's class formation. This theory enables us to reconstruct the l-cyclotomes from the absolute Galois groups of such fields. With regard to cyclotomic rigidity, under a certain assumption, we establish mono-anabelian group/monoid-theoretic reconstruction algorithms for cyclotomic rigidity isomorphisms associated to Henselian discrete valuation fields with quasi-finite residue fields [i.e., perfect residue fields whose absolute Galois groups are isomorphic to Ẑ]. As an application of the reconstructions of cyclotomic rigidity isomorphisms, we determine the structure of the groups of Galois-equivariant automorphisms of various algebraically completed multiplicative groups that arise from complete discrete valuation fields with quasi-finite residues. Moreover, as a byproduct of the argument applied in this determination [especially, in the positive characteristic case], we also determine, in a generalized situation, the structure of a certain indeterminacy “(Ind2)” that appears in S. Mochizuki's inter-universal Teichmüller theory. With regard to the Neukirch-Uchida-type result, by combining the reconstruction result of p-cyclotomes above [in the case where l = p] with a recent result due to T. Murotani, together with a computation concerning norm maps, we prove an analogous result for mixed characteristic complete discrete valuation fields whose residue fields are [strongly] p-quasi-finite and algebraic over the prime fields

Anabelian Group-theoretic Properties of the Pro-p Absolute Galois Groups of Henselian Discrete Valuation Fields

Let p be a prime number; K a Henselian discrete valuation field of characteristic 0 such that the residue field is an infinite field of characteristic p. Write GK for the absolute Galois group of K. In our previous papers, under the assumption that K contains a primitive p-th root of unity ζp, we proved that any almost pro-p-maximal quotient of GK satisfies certain “anabelian” group-theoretic properties called very elasticity and strong internal indecomposability. In the present paper, we generalize this result to the case where K does not necessarily contain ζp. Then, by applying this generalization, together with some facts concerning Hilber-tian fields, we prove the semiabsoluteness of isomorphisms between thepro-p etale fundamental groups of smooth varieties over certain classes offields of characteristic 0. Moreover, we observe that there are various sim-ilarities between the maximal pro-p quotient GpK of GK and non abelianfree pro-p groups. For instance, we verify that every topologically finitely generated closed subgroup of GpK is a free pro-p group. One of the key ingredients of our proofs is “Artin-Schreier theory in characteristic zero”introduced by MacKenzie and Whaples

Semantic Foundations of Higher-Order Probabilistic Programs in Isabelle/HOL

Higher-order probabilistic programs are used to describe statistical models and machine-learning mechanisms. The programming languages for them are equipped with three features: higher-order functions, sampling, and conditioning. In this paper, we propose an Isabelle/HOL library for probabilistic programs supporting all of those three features. We extend our previous quasi-Borel theory library in Isabelle/HOL. As a basis of the theory, we formalize s-finite kernels, which is considered as a theoretical foundation of first-order probabilistic programs and a key to support conditioning of probabilistic programs. We also formalize the Borel isomorphism theorem which plays an important role in the quasi-Borel theory. Using them, we develop the s-finite measure monad on quasi-Borel spaces. Our extension enables us to describe higher-order probabilistic programs with conditioning directly as an Isabelle/HOL term whose type is that of morphisms between quasi-Borel spaces. We also implement the qbs prover for checking well-typedness of an Isabelle/HOL term as a morphism between quasi-Borel spaces. We demonstrate several verification examples of higher-order probabilistic programs with conditioning

On Generalizations of Anabelian Group-theoretic Properties

In the present paper, we discuss certain generalizations on two anabelian group-theoretic properties --strong internal indecomposability and elasticity. More concretely, by replacing the normality conditions appearing in characterizations of strong internal indecomposability and elasticity by the subnormality conditions, we introduce the notions of strong sn-internal indecomposability and sn-elasticity and prove that various profinite groups appearing in anabelian geometry satisfy these properties