Guarded Second-Order Logic, Spanning Trees, and Network Flows

According to a theorem of Courcelle monadic second-order logic and guarded second-order logic (where one can also quantify over sets of edges) have the same expressive power over the class of all countable $k$-sparse hypergraphs. In the first part of the present paper we extend this result to hypergraphs of arbitrary cardinality. In the second part, we present a generalisation dealing with methods to encode sets of vertices by single vertices

From LTL and Limit-Deterministic B\"uchi Automata to Deterministic Parity Automata

Controller synthesis for general linear temporal logic (LTL) objectives is a challenging task. The standard approach involves translating the LTL objective into a deterministic parity automaton (DPA) by means of the Safra-Piterman construction. One of the challenges is the size of the DPA, which often grows very fast in practice, and can reach double exponential size in the length of the LTL formula. In this paper we describe a single exponential translation from limit-deterministic B\"uchi automata (LDBA) to DPA, and show that it can be concatenated with a recent efficient translation from LTL to LDBA to yield a double exponential, \enquote{Safraless} LTL-to-DPA construction. We also report on an implementation, a comparison with the SPOT library, and performance on several sets of formulas, including instances from the 2016 SyntComp competition

К вопросу об оценке противокоррозионной эффективности ингибиторов атмосферной коррозии

Розробка, дослідження захисних антикорозійних властивостей і визначення механізму дії інгібіторів атмосферної корозії, призначених для захисту металу з тонкими шарами іржі, потребує проведення натурних та прискорених корозійних випробувань. Оскільки у більшості випадків цей процес довготривалий, то для швидкого визначення антикорозійної ефективності інгібіторів корозії розроблена методика їх прискорених випробувань. Методика полягає у визначенні захисних властивостей інгібітору шляхом зняття поляризаційних кривих у нейтральному середовищі на металі з продуктами атмосферної корозії та захисною плівкою.Development, research of protective anticorrosive properties and determination of mechanism of action of atmospheric corrosion inhibitors for the protection of metal with thin layers of rust demands carrying out of the natural and accelerated corrosion tests. As in most cases this process long, for rapid determination of anticorrosive efficiency of corrosion inhibitors the new method of their accelerated tests is developed. A method consists in definition of protective ability by removal of polarization curves on a metal with the products of atmospheric corrosion and protective film in a neutral environment

Weighted Automata and Logics for Infinite Nested Words

Nested words introduced by Alur and Madhusudan are used to capture structures with both linear and hierarchical order, e.g. XML documents, without losing valuable closure properties. Furthermore, Alur and Madhusudan introduced automata and equivalent logics for both finite and infinite nested words, thus extending B\"uchi's theorem to nested words. Recently, average and discounted computations of weights in quantitative systems found much interest. Here, we will introduce and investigate weighted automata models and weighted MSO logics for infinite nested words. As weight structures we consider valuation monoids which incorporate average and discounted computations of weights as well as the classical semirings. We show that under suitable assumptions, two resp. three fragments of our weighted logics can be transformed into each other. Moreover, we show that the logic fragments have the same expressive power as weighted nested word automata.Comment: LATA 2014, 12 page

Invariant Synthesis for Incomplete Verification Engines

We propose a framework for synthesizing inductive invariants for incomplete verification engines, which soundly reduce logical problems in undecidable theories to decidable theories. Our framework is based on the counter-example guided inductive synthesis principle (CEGIS) and allows verification engines to communicate non-provability information to guide invariant synthesis. We show precisely how the verification engine can compute such non-provability information and how to build effective learning algorithms when invariants are expressed as Boolean combinations of a fixed set of predicates. Moreover, we evaluate our framework in two verification settings, one in which verification engines need to handle quantified formulas and one in which verification engines have to reason about heap properties expressed in an expressive but undecidable separation logic. Our experiments show that our invariant synthesis framework based on non-provability information can both effectively synthesize inductive invariants and adequately strengthen contracts across a large suite of programs

Symbolic Backwards-Reachability Analysis for Higher-Order Pushdown Systems

Higher-order pushdown systems (PDSs) generalise pushdown systems through the use of higher-order stacks, that is, a nested "stack of stacks" structure. These systems may be used to model higher-order programs and are closely related to the Caucal hierarchy of infinite graphs and safe higher-order recursion schemes. We consider the backwards-reachability problem over higher-order Alternating PDSs (APDSs), a generalisation of higher-order PDSs. This builds on and extends previous work on pushdown systems and context-free higher-order processes in a non-trivial manner. In particular, we show that the set of configurations from which a regular set of higher-order APDS configurations is reachable is regular and computable in n-EXPTIME. In fact, the problem is n-EXPTIME-complete. We show that this work has several applications in the verification of higher-order PDSs, such as linear-time model-checking, alternation-free mu-calculus model-checking and the computation of winning regions of reachability games

Omega-Regular Model Checking

peer reviewed"Regular model checking" is the name of a family of techniques for analyzing infinite-state systems in which states are represented by words or trees, sets of states by finite automata on these objects, and transitions by finite automata operating on pairs of state encodings, i.e. finite-state transducers. In this context, the central problem is then to compute the iterative closure of a finite-state transducer. This paper addresses the use of regular model-checking like techniques for systems whose states are represented by infinite (omega) words. Its main motivation is to show the feasibility and usefulness of this approach through a combination of the necessary theoretical developments, implementation, and experimentation. The iteration technique that is used is adapted from recent work of the authors on the iteration of finite-word transducers. It proceeds by comparing successive elements of a sequence of approximations of the iteration, detecting an "increment" that is added to move from one approximation to the next, and extrapolating the sequence by allowing arbitrary repetitions of this increment. By restricting oneself to weak deterministic Buchi automata, and using a number of implementation optimizations, examples of significant size can be handled. The proposed transducer iteration technique can just as well be exploited to compute the closure of a given set of states by the transducer iteration, which has proven to be a very effective way of using the technique. Examples such as a leaking gas burner in which time is modeled by real variables have been handled completely within the automata-theoretic setting

Senescent ground tree rewrite systems

Ground Tree Rewrite Systems with State are known to have an undecidable control state reachability problem. Taking inspiration from the recent introduction of scope-bounded multi-stack pushdown systems, we define Senescent Ground Tree Rewrite Systems. These are a restriction of ground tree rewrite systems with state such that nodes of the tree may no longer be rewritten after having witnessed an a priori fixed number of control state changes. As well as generalising scope-bounded multi-stack pushdown systems, we show --- via reductions to and from reset Petri-nets --- that these systems have an Ackermann-complete control state reachability problem. However, reachability of a regular set of trees remains undecidable