arXiv subjects

Lukáš Holík

Publications and source records attributed to Lukáš Holík.

30 records · Page 2Linked to original sources

arXiv2019

Succinct Determinisation of Counting Automata via Sphere Construction (Technical Report)

We propose an efficient algorithm for determinising counting automata (CAs), i.e., finite automata extended with bounded counters. The algorithm avoids unfolding counters into control states, unlike the naïve approach, and thus produces much smaller deterministic automata. We also develop a simplified and faster version of the general algorithm for the sub-class of so-called monadic CAs (MCAs), i.e., CAs with counting loops on character classes, which are common in practice. Our main motivation is (besides applications in verification and decision procedures of logics) the application of deterministic (M)CAs in pattern matching regular expressions with counting, which are very common in e.g. network traffic processing and log analysis. We have evaluated our algorithm against practical benchmarks from these application domains and concluded that compared to the naïve approach, our algorithm is much less prone to explode, produces automata that can be several orders of magnitude smaller, and is overall faster.

cs.FL↗

arXiv2019

Automata Terms in a Lazy WSkS Decision Procedure (Technical Report)

We propose a lazy decision procedure for the logic WSkS. It builds a term-based symbolic representation of the state space of the tree automaton (TA) constructed by the classical WSkS decision procedure. The classical decision procedure transforms the symbolic representation into a TA via a bottom-up traversal and then tests its language non-emptiness, which corresponds to satisfiability of the formula. On the other hand, we start evaluating the representation from the top, construct the state space on the fly, and utilize opportunities to prune away parts of the state space irrelevant to the language emptiness test. In order to do so, we needed to extend the notion of language terms (denoting language derivatives) used in our previous procedure for the linear fragment of the logic (the so-called WS1S) into automata terms. We implemented our decision procedure and identified classes of formulae on which our prototype implementation is significantly faster than the classical procedure implemented in the Mona tool.

cs.LO↗

arXiv2019

Deep Packet Inspection in FPGAs via Approximate Nondeterministic Automata

Deep packet inspection via regular expression (RE) matching is a crucial task of network intrusion detection systems (IDSes), which secure Internet connection against attacks and suspicious network traffic. Monitoring high-speed computer networks (100 Gbps and faster) in a single-box solution demands that the RE matching, traditionally based on finite automata (FAs), is accelerated in hardware. In this paper, we describe a novel FPGA architecture for RE matching that is able to process network traffic beyond 100 Gbps. The key idea is to reduce the required FPGA resources by leveraging approximate nondeterministic FAs (NFAs). The NFAs are compiled into a multi-stage architecture starting with the least precise stage with a high throughput and ending with the most precise stage with a low throughput. To obtain the reduced NFAs, we propose new approximate reduction techniques that take into account the profile of the network traffic. Our experiments showed that using our approach, we were able to perform matching of large sets of REs from SNORT, a popular IDS, on unprecedented network speeds.

cs.FL↗

arXiv2018

Simulation Algorithms for Symbolic Automata (Technical Report)

We investigate means of efficient computation of the simulation relation over symbolic finite automata (SFAs), i.e., finite automata with transitions labeled by predicates over alphabet symbols. In one approach, we build on the algorithm by Ilie, Navaro, and Yu proposed originally for classical finite automata, modifying it using the so-called mintermisation of the transition predicates. This solution, however, generates all Boolean combinations of the predicates, which easily causes an exponential blowup in the number of transitions. Therefore, we propose two more advanced solutions. The first one still applies mintermisation but in a local way, mitigating the size of the exponential blowup. The other one focuses on a novel symbolic way of dealing with transitions, for which we need to sacrifice the counting technique of the original algorithm (counting is used to decrease the dependency of the running time on the number of transitions from quadratic to linear). We perform a thorough experimental evaluation of all the algorithms, together with several further alternatives, showing that all of them have their merits in practice, but with the clear indication that in most of the cases, efficient treatment of symbolic transitions is more beneficial than counting.

cs.LO↗

arXiv2017

Simulations and Antichains for Efficient Handling of Finite Automata

This thesis is focused on techniques for finite automata and their use in practice, with the main emphasis on nondeterministic tree automata. This concerns namely techniques for size reduction and language inclusion testing, which are two problems that are crucial for many applications of tree automata. For size reduction of tree automata, we adapt the simulation quotient technique that is well established for finite word automata. We give efficient algorithms for computing tree automata simulations and we also introduce a new type of relation that arises from a combination of tree automata downward and upward simulation and that is very well suited for quotienting. The combination principle is relevant also for word automata. We then generalise the so called antichain universality and language inclusion checking technique developed originally for finite word automata for tree automata. Subsequently, we improve the antichain technique for both word and tree automata by combining it with the simulation-based inclusion checking techniques, significantly improving efficiency of the antichain method. We then show how the developed reduction and inclusion checking methods improve the method of abstract regular tree model checking, the method that was the original motivation for starting the work on tree automata. Both the reduction and the language inclusion methods are based on relatively simple and general principles that can be further extended for other types of automata and related formalisms. An example is our adaptation of the reduction methods for alternating Büchi automata, which results in an efficient alternating automata size reduction technique.

cs.FL↗

arXiv2017

Effect Summaries for Thread-Modular Analysis

We propose a novel guess-and-check principle to increase the efficiency of thread-modular verification of lock-free data structures. We build on a heuristic that guesses candidates for stateless effect summaries of programs by searching the code for instances of a copy-and-check programming idiom common in lock-free data structures. These candidate summaries are used to compute the interference among threads in linear time. Since a candidate summary need not be a sound effect summary, we show how to fully automatically check whether the precision of candidate summaries is sufficient. We can thus perform sound verification despite relying on an unsound heuristic. We have implemented our approach and found it up to two orders of magnitude faster than existing ones.

cs.PL↗

arXiv2017

Lazy Automata Techniques for WS1S

We present a new decision procedure for the logic WS1S. It originates from the classical approach, which first builds an automaton accepting all models of a formula and then tests whether its language is empty. The main novelty is to test the emptiness on the fly, while constructing a symbolic, term-based representation of the automaton, and prune the constructed state space from parts irrelevant to the test. The pruning is done by a generalization of two techniques used in antichain-based language inclusion and universality checking of finite automata: subsumption and early termination. The richer structure of the WS1S decision problem allows us, however, to elaborate on these techniques in novel ways. Our experiments show that the proposed approach can in many cases significantly outperform the classical decision procedure (implemented in the MONA tool) as well as recently proposed alternatives.

cs.LO↗

arXiv2016

Proceedings 11th Doctoral Workshop on Mathematical and Engineering Methods in Computer Science

MEMICS provides a forum for doctoral students interested in applications of mathematical and engineering methods in computer science. Besides a rich technical programme (including invited talks, regular papers, and presentations), MEMICS also offers friendly social activities and exciting opportunities for meeting like-minded people. MEMICS submissions traditionally cover all areas of computer science (such as parallel and distributed computing, computer networks, modern hardware and its design, non-traditional computing architectures, information systems and databases, multimedia and graphics, verification and testing, computer security, as well as all related areas of theoretical computer science).

cs.LO↗

arXiv2016

Summaries for Context-Free Games

We study two-player games played on the infinite graph of sentential forms induced by a context-free grammar (that comes with an ownership partitioning of the non-terminals). The winning condition is inclusion of the derived terminal word in the language of a finite automaton. Our contribution is a new algorithm to decide the winning player and to compute her strategy. It is based on a novel representation of all plays starting in a non-terminal. The representation uses the domain of Boolean formulas over the transition monoid of the target automaton. The elements of the monoid are essentially procedure summaries, and our approach can be seen as the first summary-based algorithm for the synthesis of recursive programs. We show that our algorithm has optimal (doubly exponential) time complexity, that it is compatible with recent antichain optimizations, and that it admits a lazy evaluation strategy. Our preliminary experiments indeed show encouraging results, indicating a speed up of three orders of magnitude over a competitor.

cs.LO↗

arXiv2016

Reduction of Nondeterministic Tree Automata

We present an efficient algorithm to reduce the size of nondeterministic tree automata, while retaining their language. It is based on new transition pruning techniques, and quotienting of the state space w.r.t. suitable equivalences. It uses criteria based on combinations of downward and upward simulation preorder on trees, and the more general downward and upward language inclusions. Since tree-language inclusion is EXPTIME-complete, we describe methods to compute good approximations in polynomial time. We implemented our algorithm as a module of the well-known libvata tree automata library, and tested its performance on a given collection of tree automata from various applications of libvata in regular model checking and shape analysis, as well as on various classes of randomly generated tree automata. Our algorithm yields substantially smaller and sparser automata than all previously known reduction techniques, and it is still fast enough to handle large instances.

cs.FL↗

arXiv2015

Pointer Race Freedom

We propose a novel notion of pointer race for concurrent programs manipulating a shared heap. A pointer race is an access to a memory address which was freed, and it is out of the accessor's control whether or not the cell has been re-allocated. We establish two results. (1) Under the assumption of pointer race freedom, it is sound to verify a program running under explicit memory management as if it was running with garbage collection. (2) Even the requirement of pointer race freedom itself can be verified under the garbage-collected semantics. We then prove analogues of the theorems for a stronger notion of pointer race needed to cope with performance-critical code purposely using racy comparisons and even racy dereferences of pointers. As a practical contribution, we apply our results to optimize a thread-modular analysis under explicit memory management. Our experiments confirm a speed-up of up to two orders of magnitude.

cs.PL↗

arXiv2015

From Low-Level Pointers to High-Level Containers

We propose a method that transforms a C program manipulating containers using low-level pointer statements into an equivalent program where the containers are manipulated via calls of standard high-level container operations like push_back or pop_front. The input of our method is a C program annotated by a special form of shape invariants which can be obtained from current automatic shape analysers after a slight modification. The resulting program where the low-level pointer statements are summarized into high-level container operations is more understandable and (among other possible benefits) better suitable for program analysis. We have implemented our approach and successfully tested it through a number of experiments with list-based containers, including experiments with simplification of program analysis by separating shape analysis from analysing data-related properties.

cs.PL↗