Languages of Dot-depth One over Infinite Words

Over finite words, languages of dot-depth one are expressively complete for alternation-free first-order logic. This fragment is also known as the Boolean closure of existential first-order logic. Here, the atomic formulas comprise order, successor, minimum, and maximum predicates. Knast (1983) has shown that it is decidable whether a language has dot-depth one. We extend Knast's result to infinite words. In particular, we describe the class of languages definable in alternation-free first-order logic over infinite words, and we give an effective characterization of this fragment. This characterization has two components. The first component is identical to Knast's algebraic property for finite words and the second component is a topological property, namely being a Boolean combination of Cantor sets. As an intermediate step we consider finite and infinite words simultaneously. We then obtain the results for infinite words as well as for finite words as special cases. In particular, we give a new proof of Knast's Theorem on languages of dot-depth one over finite words.Comment: Presented at LICS 201

Second-Order Hyperproperties

We introduce Hyper$^2$LTL, a temporal logic for the specification of hyperproperties that allows for second-order quantification over sets of traces. Unlike first-order temporal logics for hyperproperties, such as HyperLTL, Hyper$^2$LTL can express complex epistemic properties like common knowledge, Mazurkiewicz trace theory, and asynchronous hyperproperties. The model checking problem of Hyper$^2$LTL is, in general, undecidable. For the expressive fragment where second-order quantification is restricted to smallest and largest sets, we present an approximate model-checking algorithm that computes increasingly precise under- and overapproximations of the quantified sets, based on fixpoint iteration and automata learning. We report on encouraging experimental results with our model-checking algorithm, which we implemented in the tool~\texttt{HySO}

Fragments of first-order logic over infinite words

We give topological and algebraic characterizations as well as language theoretic descriptions of the following subclasses of first-order logic FO[<] for omega-languages: Sigma_2, FO^2, the intersection of FO^2 and Sigma_2, and Delta_2 (and by duality Pi_2 and the intersection of FO^2 and Pi_2). These descriptions extend the respective results for finite words. In particular, we relate the above fragments to language classes of certain (unambiguous) polynomials. An immediate consequence is the decidability of the membership problem of these classes, but this was shown before by Wilke and Bojanczyk and is therefore not our main focus. The paper is about the interplay of algebraic, topological, and language theoretic properties.Comment: Conference version presented at 26th International Symposium on Theoretical Aspects of Computer Science, STACS 200

It Is Easy to Be Wise After the Event: Communicating Finite-State Machines Capture First-Order Logic with "Happened Before"

Message sequence charts (MSCs) naturally arise as executions of communicating finite-state machines (CFMs), in which finite-state processes exchange messages through unbounded FIFO channels. We study the first-order logic of MSCs, featuring Lamport\u27s happened-before relation. We introduce a star-free version of propositional dynamic logic (PDL) with loop and converse. Our main results state that (i) every first-order sentence can be transformed into an equivalent star-free PDL sentence (and conversely), and (ii) every star-free PDL sentence can be translated into an equivalent CFM. This answers an open question and settles the exact relation between CFMs and fragments of monadic second-order logic. As a byproduct, we show that first-order logic over MSCs has the three-variable property

A Proof of the Factorization Forest Theorem

We show that for every homomorphism $\Gamma^+ \to S$ where $S$ is a finite semigroup there exists a factorization forest of height \leq 3 \abs{S}. The proof is based on Green's relations.Comment: 4 page

The expressive power of simple logical fragments over traces

We compare the expressive power of some first-order fragments and of two simple temporal logics over Mazurkiewicz traces. Over words, most of these fragments have the same expressive power whereas over traces we show that the ability of formulating concurrency increases the expressive power. We also show that over so-called dependence structures it is impossible to formulate concurrency with the first-order fragments under consideration. Although the first-order fragments $\Delta_n[<]$ and $FO^2[<]$ over partial orders both can express concurrency of two actions, we show that in general they are incomparable over traces. For $FO^2[<]$ we give a characterization in terms of temporal logic by allowing an operator for parallelism

Verification and Enforcement of Safe Schedules for Concurrent Programs

Automated software verification can prove the correctness of a program with respect to a given specification and may be a valuable support in the difficult task of ensuring the quality of large software systems. However, the automated verification of concurrent software can be particularly challenging due to the vast complexity that non-deterministic scheduling causes. This thesis is concerned with techniques that reduce the complexity of concurrent programs in order to ease the verification task. We approach this problem from two orthogonal directions: state space reduction and reduction of non-determinism in executions of concurrent programs. Following the former direction, we present an algorithm for dynamic partial-order reduction, a state space reduction technique that avoids the verification of redundant executions. Our algorithm, EPOR, eagerly creates schedules for program fragments. In comparison to other dynamic partial-order reduction algorithms, it avoids redundant race and dependency checks. Our experiments show that EPOR runs considerably faster than a state-of-the-art algorithm, which allows in several cases to analyze programs with a higher number of threads within a given timeout. In the latter direction, we present a formal framework for using incomplete verification results to extract safe schedulers. As incomplete verification results do not need to proof the correctness of all possible executions of a program, their complexity can be significantly lower than complete verification results. Hence, they can be faster obtained. We constrain the scheduling of programs but not their inputs in order to preserve their full functionality. In our framework, executions under the scheduling constraints of an incomplete verification result are safe, deadlock-free, and fair. We instantiate our framework with the Impact model checking algorithm and find in our evaluation that it can be used to model check programs that are intractable for monolithic model checkers, synthesize synchronization via assume statements, and guarantee fair executions. In order to safely execute a program within the set of executions covered by an incomplete verification, scheduling needs to be constrained. We discuss how to extract and encode schedules from incomplete verification results, for both finite and infinite executions, and how to efficiently enforce scheduling constraints, both in terms of reducing the time to look up permission of executing the next event and executing independent events concurrently (by applying partial-order reduction). A drawback of enforcing scheduling constraints is a potential overhead in the execution time. However, in several cases, constrained executions turned out to be even faster than unconstrained executions. Our experimental results show that iteratively relaxing a schedule can significantly reduce this overhead. Hence, it is possible to adjust the incurred execution time overhead in order to find a sweet spot with respect to the amount of effort for creating schedules (i.e., the duration of verification). Interestingly, we found cases in which a much earlier reduction of execution time overhead is obtained by choosing favorable scheduling constraints, which suggests that execution time performance does not simply rely on the number of scheduling constraints but to a large extend also on their structure

Kartiranje krških formacija ispod povijesne zgrade u Szydłówu u Poljskoj pomoću georadara

The Mid-Poland Uplands Belt is a vast area characterized by the presence of carbonate and sulphate rocks. In some parts of this region karst forming and developing processes are dynamic in character. The studied area is the terrain around a historic church in a small village of Szydłów. The building is situated on a hill which is formed by Sarmatian detrital limestone undergoing karst processes. At the foot of the hill there is a number of small caves. Characteristic geological structure and land transformations that are present due to the karst processes prompted the authors to conduct a GPR survey. The aim of this study was to verify whether there is a continuation of caves in the area around the monument. An analysis was made to estimate the risk of damaging the historic building due to the ongoing karst processes. The authors obtained good quality results from GPR measurements. The results confirmed the existence of unknown voids and loosening in rock structure. On radargrams, the authors recorded stratum mapping which confirms the existence of gravitational loosening of the rock mass near the cave ceilings and walls. The results prove that the GPR is an appropriate instrument for mapping some of the karst structures and evaluation of the orogen stability.Brdski pojas u srednjoj Poljskoj veliko je područje u kojem prevladavaju karbonatne i sulfatne stijene. U nekim su dijelovima ove procesi okršavanja dinamičkog karaktera. Proučavan je teren oko povijesne crkve u Szydłówu. Građevina se nalazi na brdu koje je formirano procesima karstifikacije klastičnih vapnenaca sarmata. U podnožju brda ima nekoliko malih špilja. Karakteristične geološke strukture i transformacije terena koje su posljedica karstifikacije potaknule su autore da provedu istraživanja georadarom. Cilj je ove studije verificirati postojanje špilja i u prostoru oko spomenika. Napravljena je analiza rizika oštećenja spomenika krškim procesima. Mjerenjima georadarom dobijeni su dobri rezultati koji potvrđuju postojanje do sada nepoznatih šupljina i oslabljenih stijenskih struktura. Prema zabilježenim radarogramima autori su potvrdili da dolazi do gravitacijskig slabljenja stijenske mase u blizini stropa i zidova špilja. Rezultati dokazuju da je georadar prikladan instrument za kartiranje nekih krških struktura i procjenu stabilnosti stijena