### Book chapter

## On the Complexity of Pointer Arithmetic in Separation Logic.

We investigate the complexity consequences of adding pointer arithmetic to separation logic. Specifically, we study an extension of the points-to fragment of symbolic-heap separation logic with sets of simple “difference constraints” of the form *x*≤*y*+*k*

, where *x* and *y* are pointer variables and *k* is an integer offset. This extension can be considered a practically minimal language for separation logic with pointer arithmetic.

Most significantly, we find that, even for this minimal language, polynomial-time decidability is already impossible: satisfiability becomes NP

-complete, while quantifier-free entailment becomes coNP-complete and quantified entailment becomes *Π**P*2-complete (where *Π**P*2

is the second class in the polynomial-time hierarchy).

However, the language does satisfy the small model property, meaning that any satisfiable formula has a model, and any invalid entailment has a countermodel, of polynomial size, whereas this property fails when richer forms of arithmetical constraints are permitted.

### In book

In this article, we investigate the logical structure of memory models of theoretical and practical interest. Our main interest is in “the logic behind a fixed memory model”, rather than in “a model of any kind behind a given logical system”. As an effective language for reasoning about such memory models, we use the formalism of separation logic. Our main result is that for any concrete choice of heap-like memory model, validity in that model is *undecidable* even for purely propositional formulas in this language.

The main novelty of our approach to the problem is that we focus on validity in specific, concrete memory models, as opposed to validity in general classes of models.

Besides its intrinsic technical interest, this result also provides new insights into the nature of their decidable fragments. In particular, we show that, in order to obtain such decidable fragments, either the formula language must be severely restricted or the valuations of propositional variables must be constrained.

In addition, we show that a number of propositional systems that approximate separation logic are undecidable as well. In particular, this resolves the open problems of decidability for Boolean BI and Classical BI.

Moreover, we provide one of the simplest undecidable propositional systems currently known in the literature, called “Minimal Boolean BI”, by combining the purely positive implication-conjunction fragment of Boolean logic with the laws of multiplicative *-conjunction, its unit and its adjoint implication, originally provided by intuitionistic multiplicative linear logic. Each of these two components is individually decidable: the implication-conjunction fragment of Boolean logic is co-NP-complete, and intuitionistic multiplicative linear logic is NP-complete.

All of our undecidability results are obtained by means of a direct encoding of Minsky machines.

Key Words and Phrases: Separation logic, undecidability, memory models, bunched logic

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.

In a collaborative system, the agents collaborate to achieve a common goal, but they are not willing to share some sensitive private information.

The question is how much damage can be done by a malicious participant sitting inside the system.

We assume that all the participants (including internal adversaries) have bounded memory – at any moment, they can store only a fixed number of messages of a fixed size. The Dolev–Yao adversaries can compose, decompose, eavesdrop, and intercept messages, and create fresh values (nonces), but within their bounded memory.

We prove that the secrecy problem is PSPACE-complete in the bounded memory model where all actions are balanced and a potentially infinite number of the nonce updates is allowed.

We also show that the well-known security protocol anomalies (starting from the Lowe attack to the Needham–Schroeder protocol) can be rephrased within the bounded memory paradigm with the explicit memory bounds.

Heaps are well-studied fundamental data structures, having myriads of applications, both theoretical and practical. We consider the problem of designing a heap with an “optimal” extract-min operation. Assuming an arbitrary linear ordering of keys, a heap with n elements typically takes O(log n) time to extract the min-imum. Extracting all elements faster is impossible as this would violate the Ω(n log n) bound for comparison-based sorting. It is known, however, that is takes only O(n + k log k) time to sort just k smallest elements out of n given, which prompts that there might be a faster heap, whose extract-min performance depends on the number of elements extracted so far. In this paper we show that is indeed the case. We present a version of heap that performs insert in O(1) time and takes only O(log ∗ n + log k) time to carry out the k-th extraction (where log ∗ denotes the iterated logarithm). All the above bounds are worst-case.

Modern cybernetics and computer engineering papers and topics are presented in the proceedings. This proceedings is a Vol. 3 of the Computer Science On-line Conference proceedings. Papers in this part discuss modern cybernetics and applied informatics in technical systems. This book constitutes the refereed proceedings of the Applied Informatics and Cybernetics in Intelligent Systems section of the 9th Computer Science On-line Conference 2020 (CSOC 2020), held on-line in April 2020. CSOC 2020 has received (all sections) more than 270 submissions from more than 35 countries. More than 65% of accepted submissions were received from Europe, 21% from Asia, 8% from Africa, 4% from America and 2% from Australia. CSOC 2020 conference intends to provide an international forum for the discussion of the latest high-quality research results in all areas related to Computer Science. Computer Science On-line Conference is held on-line, and modern communication technology, which are broadly used, improves the traditional concept of scientific conferences. It brings equal opportunity to participate for all researchers around the world.

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.

Data management and analysis is one of the fastest growing and most challenging areas of research and development in both academia and industry. Numerous types of applications and services have been studied and re-examined in this field resulting in this edited volume which includes chapters on effective approaches for dealing with the inherent complexity within data management and analysis. This edited volume contains practical case studies, and will appeal to students, researchers and professionals working in data management and analysis in the business, education, healthcare, and bioinformatics areas.