### Article

## Bounded memory protocols

It is well-known that the Dolev–Yao adversary is a powerful adversary. Besides acting as the network, intercepting, decomposing, composing and sending messages, he can remember as much information as he needs. That is, his memory is unbounded. We recently proposed a weaker Dolev–Yao like adversary, which also acts as the network, but whose memory is bounded. We showed that this Bounded Memory Dolev–Yao adversary, when given enough memory, can carry out many existing protocol anomalies. In particular, the known anomalies arise for bounded memory protocols, where although the total number of sessions is unbounded, there are only a bounded number of concurrent sessions and the honest participants of the protocol cannot remember an unbounded number of facts or an unbounded number of nonces at a time. This led us to the question of whether it is possible to infer an upper-bound on the memory required by the Dolev–Yao adversary to carry out an anomaly from the memory restrictions of the bounded protocol. This paper answers this question negatively (Theorem 8).

An attempt to critically analyze the claims of the theory of self-organization of complex systems (synergetics) to the interdisciplinary generalizations and the universal efficacy of its models is made in the paper. The grounds of transfer of synergetic models to different disciplinary fields are under discussion. It is argued that synergetics is rather a mental scheme or a heuristic approach to exploring the complex behavior of systems, than a universal key to solving concrete scientific problems. Some prospects of development and the possible future of synergetics within the next decades are estimated.

We establish foundational results on the computational complexity of deciding entailment in Separation Logic with general inductive predicates whose underlying base language allows for pure formulas, pointers and existentially quantified variables. We show that entailment is in general undecidable, and ExpTime-hard in a fragment recently shown to be decidable by Iosif *et al.* Moreover, entailment in the base language is PI_2^p complete, the upper bound even holds in the presence of list predicates. We additionally show that entailment in essentially any fragment of Separation Logic allowing for general inductive predicates is intractable even when strong syntactic restrictions are imposed.

The author argues on expediency and mutual conditionality of evolutionary changes in the nature and in society. In the article three major factors of the evolution are allocated, namely: the accident, the factor of coincidence of circumstances and the factor of acceleration of social evolution.

The phenomenon of communication as a manifestation of complexity of interacting creatures. Communication is considered not as a privilege of a human being; it is shown that it is rooted in the world of living nature, it has an evolutionary origins. Communicative complexity is exposed by such concepts as flexibility, constructing, intersubjectivity, participatory sense-making, empathy, synergy, mutual incorporation and co-emergence of creatures which enter the process of communication. Understanding of communication from the position of the conception of enactivism allows disclosing some substantial aspects of the constructivist character of communicative interaction.

The conference *Philosophy, Mathematics, Linguistics: Aspects of Interaction 2014 (PhML-2014)* is a sequel in the series of conferences intended to provide a forum for philosophers, mathematicians, linguists, logicians, and computer scientists who share an interest in cross-disciplinary research. The conference PhML-2014 is endorsed by the American National Committee of the Division of Logic, Methodology and Philosophy of Science (DLMPS) of the International Union of the History and Philosophy of Science (IUHPS), the Japan Association for Philosophy of Science, the Swedish National Committee for Logic, Methodology and Philosophy of Science.

The monograph is devoted to the consideration of complex systems from the position of the end the 21st century. The considerable breakthrough in the understanding of complex systems is comprehensively analyzed. Such a breakthrough is connected with the use of the newest methods of nonlinear dynamics, of organization of the modern computational experiments. The book is meant for specialists in different fields of natural sciences and the humanities as well as for all readers who are interested in the recent advancements in science.

It is well-known that the Dolev-Yao adversary is a powerful adversary. Besides acting as the network, intercepting, sending, and composing messages, he can remember as much information as he needs. That is, his memory is unbounded.

We recently proposed a weaker Dolev-Yao like adversary, which also acts as the network, but whose memory is bounded. We showed that this Bounded Memory Dolev-Yao adversary, when given enough memory, can carry out many existing protocol anomalies. In particular, the known anomalies arise for *bounded memory protocols*, where there is only a bounded number of concurrent sessions and the honest participants of the protocol cannot remember an unbounded number of facts nor an unbounded number of nonces at a time. This led us to the question of whether it is possible to infer an upper-bound on the memory required by the Dolev-Yao adversary to carry out an anomaly from the memory restrictions of the bounded protocol. This paper answers this question negatively (Theorem 2).

The second contribution of this paper is the formalization of Progressing Collaborative Systems that may create fresh values, such as nonces. In this setting there is no unbounded adversary, although bounded memory adversaries may be present. We prove the NP-completeness of the reachability problem for Progressing Collaborative Systems that may create fresh values.

We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.

We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.

We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.

This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.