Showing papers on "Pushdown automaton published in 2020"
08 Jul 2020
TL;DR: These are automata whose nondeterminism can be resolved based on the run constructed thus far and it follows that the universality problem for ω-GFG-PDA is in EXPTIME as well.
Abstract: We introduce good-for-games ω-pushdown automata (ω-GFG-PDA). These are automata whose nondeterminism can be resolved based on the run constructed thus far. Good-for-gameness enables automata to be composed with games, trees, and other automata, applications which otherwise require deterministic automata. Our main results are that ω-GFG-PDA are more expressive than deterministic ω-pushdown automata and that solving infinite games with winning conditions specified by ω-GFG-PDA is EXPTIME-complete. Thus, we have identified a new class of ω-contextfree winning conditions for which solving games is decidable. It follows that the universality problem for ω-GFG-PDA is in EXPTIME as well. Moreover, we study closure properties of the class of languages recognized by ω-GFG-PDA and decidability of good-for-gameness of ω-pushdown automata and languages.
19 citations
TL;DR: A vectorial kernel method is developed which solves in a unified framework all the problems related to the enumeration of words generated by a pushdown automaton for the enumerations of lattice paths that avoid a fixed word (a pattern), or for counting the occurrences of a given pattern.
Abstract: In this article we develop a vectorial kernel method—a powerful method which solves in a unified framework all the problems related to the enumeration of words generated by a pushdown automaton. We apply it for the enumeration of lattice paths that avoid a fixed word (a pattern), or for counting the occurrences of a given pattern. We unify results from numerous articles concerning patterns like peaks, valleys, humps, etc., in Dyck and Motzkin paths. This refines the study by Banderier and Flajolet from 2002 on enumeration and asymptotics of lattice paths: we extend here their results to pattern-avoiding walks/bridges/meanders/excursions. We show that the autocorrelation polynomial of this forbidden pattern, as introduced by Guibas and Odlyzko in 1981 in the context of rational languages, still plays a crucial role for our algebraic languages. En passant, our results give the enumeration of some classes of self-avoiding walks, and prove several conjectures from the On-Line Encyclopedia of Integer Sequences. Finally, we also give the trivariate generating function (length, final altitude, number of occurrences of the pattern p), and we prove that the number of occurrences is normally distributed and linear with respect to the length of the walk: this is what Flajolet and Sedgewick call an instance of Borges’s theorem.
18 citations
TL;DR: Good-for-games pushdown automata as discussed by the authors enable automata to be composed with games, trees, and other automata, applications which otherwise require deterministic automata and are more expressive than deterministic $-pushdown pushdown PDA.
Abstract: We introduce good-for-games $\omega$-pushdown automata ($\omega$-GFG-PDA). These are automata whose nondeterminism can be resolved based on the input processed so far. Good-for-gameness enables automata to be composed with games, trees, and other automata, applications which otherwise require deterministic automata. Our main results are that $\omega$-GFG-PDA are more expressive than deterministic $\omega$- pushdown automata and that solving infinite games with winning conditions specified by $\omega$-GFG-PDA is EXPTIME-complete. Thus, we have identified a new class of $\omega$-contextfree winning conditions for which solving games is decidable. It follows that the universality problem for $\omega$-GFG-PDA is in EXPTIME as well. Moreover, we study closure properties of the class of languages recognized by $\omega$-GFG- PDA and decidability of good-for-gameness of $\omega$-pushdown automata and languages. Finally, we compare $\omega$-GFG-PDA to $\omega$-visibly PDA, study the resources necessary to resolve the nondeterminism in $\omega$-GFG-PDA, and prove that the parity index hierarchy for $\omega$-GFG-PDA is infinite.
14 citations
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TL;DR: The third version of Automata Tutor as discussed by the authors supports automated grading and feedback generation for a greatly extended variety of new problems, including problems that ask students to create regular expressions, context-free grammars, pushdown automata and Turing machines corresponding to a given description, and problems about converting between equivalent models.
Abstract: Computer science class enrollments have rapidly risen in the past decade. With current class sizes, standard approaches to grading and providing personalized feedback are no longer possible and new techniques become both feasible and necessary. In this paper, we present the third version of Automata Tutor, a tool for helping teachers and students in large courses on automata and formal languages. The second version of Automata Tutor supported automatic grading and feedback for finite-automata constructions and has already been used by thousands of users in dozens of countries. This new version of Automata Tutor supports automated grading and feedback generation for a greatly extended variety of new problems, including problems that ask students to create regular expressions, context-free grammars, pushdown automata and Turing machines corresponding to a given description, and problems about converting between equivalent models - e.g., from regular expressions to nondeterministic finite automata. Moreover, for several problems, this new version also enables teachers and students to automatically generate new problem instances. We also present the results of a survey run on a class of 950 students, which shows very positive results about the usability and usefulness of the tool.
13 citations
23 Nov 2020
TL;DR: An automated what-if analysis tool AalWiNes for MPLS networks which allows us to verify both logical properties as well as quantitative properties under multiple link failures by several orders of magnitude.
Abstract: We present an automated what-if analysis tool AalWiNes for MPLS networks which allows us to verify both logical properties (e.g., related to the policy compliance) as well as quantitative properties (e.g., concerning the latency) under multiple link failures. Our tool relies on weighted pushdown automata, a quantitative extension of classic automata theory, and takes into account the actual dataplane configuration, rendering it especially useful for debugging. In particular, our tool collects the different router forwarding tables and then builds a pushdown system, on which quantitative reachability is performed based on an expressive query language. Our experiments show that our tool outperforms state-of-the-art approaches (which until now have been restricted to logical properties) by several orders of magnitude; furthermore, our quantitative extension only entails a moderate overhead in terms of runtime. The tool comes with a platform-independent user interface and is publicly available as open-source, together with all other experimental artefacts.
13 citations
TL;DR: By chemically reconfiguring them to recognize representative languages in the lower classes of the Chomsky hierarchy, this work illustrates the inclusiveness of the hierarchy of native chemical automata and opens the door for chemical programming without biochemistry.
Abstract: Living systems process information using chemistry. Computations can be viewed as language recognition problems where both languages and automata recognizing them form an inclusive hierarchy. Chemical realizations, without using biochemistry, of the main classes of computing automata, Finite Automata (FA), 1-stack Push Down Automata (1-PDA) and Turing Machine (TM) have recently been presented. These use chemistry for the representation of input information, its processing and output information. The Turing machine uses the Belousov-Zhabotinsky (BZ) oscillatory reaction to recognize a representative Context-Sensitive Language (CSL), the 1-PDA uses a pH network to recognize a Context Free Language (CFL) and a FA for a Regular Language (RL) uses a precipitation reaction. By chemically reconfiguring them to recognize representative languages in the lower classes of the Chomsky hierarchy we illustrate the inclusiveness of the hierarchy of native chemical automata. These examples open the door for chemical programming without biochemistry. Furthermore, the thermodynamic metric originally introduced to identify the accept/reject state of the chemical output for the CSL, can equally be used for recognizing CFL and RL by the automata. Finally, we point out how the chemical and thermodynamic duality of accept/reject criteria can be used in the optimization of the energetics and efficiency of computations.
12 citations
Posted Content•
TL;DR: A neural network is built specifically structured like a PDA, where weights correspond directly to the PDA rules, and this model and method of proof can be generalized to other state machines, such as a Turing Machine.
Abstract: Given a collection of strings belonging to a context free grammar (CFG) and another collection of strings not belonging to the CFG, how might one infer the grammar? This is the problem of grammatical inference. Since CFGs are the languages recognized by pushdown automata (PDA), it suffices to determine the state transition rules and stack action rules of the corresponding PDA. An approach would be to train a recurrent neural network (RNN) to classify the sample data and attempt to extract these PDA rules. But neural networks are not a priori aware of the structure of a PDA and would likely require many samples to infer this structure. Furthermore, extracting the PDA rules from the RNN is nontrivial. We build a RNN specifically structured like a PDA, where weights correspond directly to the PDA rules. This requires a stack architecture that is somehow differentiable (to enable gradient-based learning) and stable (an unstable stack will show deteriorating performance with longer strings). We propose a stack architecture that is differentiable and that provably exhibits orbital stability. Using this stack, we construct a neural network that provably approximates a PDA for strings of arbitrary length. Moreover, our model and method of proof can easily be generalized to other state machines, such as a Turing Machine.
10 citations
TL;DR: In this paper, the Hartmanis-Stearns problem for integer base expansions of algebraic irrational real numbers was studied from a computational point of view, and it was shown that the base-b expansion of an algebraic real number cannot be generated by a deterministic pushdown automaton.
Abstract: — We consider the complexity of integer base expansions of algebraic irrational numbers from a computational point of view. We show that the Hartmanis–Stearns problem can be solved in a satisfactory way for the class of multistack machines. In this direction, our main result is that the base-b expansion of an algebraic irrational real number cannot be generated by a deterministic pushdown automaton. We also confirm an old claim of Cobham proving that such numbers cannot be generated by a tag machine with dilation factor larger than one.
7 citations
28 Dec 2020
TL;DR: It is proved that non-self-embedding grammars and constant-height pushdown automata are polynomially related in size and the converse transformation is proved to cost exponential.
Abstract: Non-self-embedding grammars are a restriction of context-free grammars which does not allow to describe recursive structures and, hence, which characterizes only the class of regular languages. A double exponential gap in size from non-self-embedding grammars to deterministic finite automata is known. The same size gap is also known from constant-height pushdown automata and 1-limited automata to deterministic finite automata. Constant-height pushdown automata and 1-limited automata are compared with non-self-embedding grammars. It is proved that non-self-embedding grammars and constant-height pushdown automata are polynomially related in size. Furthermore, a polynomial size simulation by 1-limited automata is presented. However, the converse transformation is proved to cost exponential.
7 citations
01 Nov 2020
TL;DR: In this paper, a differentiable stack data structure is proposed to simultaneously encode an exponential number of stack configurations, based on Lang's algorithm for simulating non-deterministic pushdown automata.
Abstract: We present a differentiable stack data structure that simultaneously and tractably encodes an exponential number of stack configurations, based on Lang’s algorithm for simulating nondeterministic pushdown automata. We call the combination of this data structure with a recurrent neural network (RNN) controller a Nondeterministic Stack RNN. We compare our model against existing stack RNNs on various formal languages, demonstrating that our model converges more reliably to algorithmic behavior on deterministic tasks, and achieves lower cross-entropy on inherently nondeterministic tasks.
7 citations
01 Apr 2020
TL;DR: In this article, the decidability of the model checking problem for recursion schemes against properties defined by alternating B-automata, an extension of alternating parity automata for infinite trees with a boundedness acceptance condition, was shown.
Abstract: Higher-order recursion schemes are an expressive formalism used to define languages of possibly infinite ranked trees They extend regular and context-free grammars, and are equivalent to simply typed λY-calculus and collapsible pushdown automata In this work we prove, under a syntactical constraint called safety, decidability of the model-checking problem for recursion schemes against properties defined by alternating B-automata, an extension of alternating parity automata for infinite trees with a boundedness acceptance condition We then exploit this result to show how to compute downward closures of languages of finite trees recognized by safe recursion schemes
TL;DR: This work presents a second-order logic with the same expressive power as Buchi or Muller pushdown automata for infinite words and extends fundamental logical characterizations of Buchi, Elgot, Trakhtenbrot for regular languages of finite and infinite words to ω-context-free languages.
Abstract: Context-free languages of infinite words have recently found increasing interest. Here, we will present a second-order logic with the same expressive power as Buchi or Muller pushdown automata for infinite words. This extends fundamental logical characterizations of Buchi, Elgot, Trakhtenbrot for regular languages of finite and infinite words and a more recent logical characterization of Lautemann, Schwentick and Therien for context-free languages of finite words to ω-context-free languages. For our argument, we will investigate Greibach normal forms of ω-context-free grammars as well as a new type of Buchi pushdown automata which can alter their stack by at most one element and without ϵ-transitions. We show that they suffice to accept all ω-context-free languages. This enables us to use similar results recently developed for infinite nested words.
TL;DR: The Timed k-Tail specification mining technique is addressed, which can mine finite state models that capture both the functional and timing behavior of a software system from execution traces and outperforms state-of-the-art techniques in terms of scalability and accuracy of the mined models.
Abstract: To mitigate the cost of manually producing and maintaining models capturing software specifications, specification mining techniques can be exploited to automatically derive up-to-date models that faithfully represent the behavior of software systems. So far, specification mining solutions focused on extracting information about the functional behavior of the system, especially in the form of models that represent the ordering of the operations. Well-known examples are finite state models capturing the usage protocol of software interfaces and temporal rules specifying relations among system events. Although the functional behavior of a software system is a primary aspect of concern, there are several other non-functional characteristics that must be typically addressed jointly with the functional behavior of a software system. Efficiency is one of the most relevant characteristics. Indeed, an application that delivers the right functionalities with an inefficient implementation may fail to satisfy the expectations of its users. Interestingly, the timing behavior is strongly dependent on the functional behavior of a software system. For instance, the timing of an operation depends on the functional complexity and size of the computation that is performed. Consequently, models that combine the functional and timing behaviors, as well as their dependencies, are extremely important to precisely reason on the behavior of software systems. In this paper, we address the challenge of generating models that capture both the functional and timing behavior of a software system from execution traces. The result is the Timed k-Tail (TkT) specification mining technique, which can mine finite state models that capture such an interplay: the functional behavior is represented by the possible order of the events accepted by the transitions, while the timing behavior is represented through clocks and clock constraints of different nature associated with transitions. Our empirical evaluation with several libraries and applications shows that TkT can generate accurate models, capable of supporting the identification of timing anomalies due to overloaded environment and performance faults. Furthermore, our study shows that TkT outperforms state-of-the-art techniques in terms of scalability and accuracy of the mined models.
TL;DR: The problem if a given configuration of a pushdown automaton (PDA) is bisimilar with some (unspecified) finite-state process is shown to be decidable, and the decidability is proven in the framework of first-order grammars, which are given by finite sets of labelled rules that rewrite roots offirst-order terms.
TL;DR: Acceptance by empty stack and acceptance by final states are proven to have the same recognition power in this new model, which includes the class of context-free languages.
Journal Article•
TL;DR: The goal of this work is to provide an overview of old and recent work on these formal systems from a descriptional complexity perspective, that is the study of the relationships between the sizes of such devices.
Abstract: It is well known that regular (or Type 3) languages are equivalent to finite automata. Nevertheless, many other characterizations of this class of lan- guages in terms of computational devices and generative models are present in the literature. For example, by suitably restricting more general models such as context-free grammars, pushdown automata, and Turing machines, that characterize wider classes of languages, it is possible to obtain formal models that generate or recognize regular languages only. These restricted formalisms provide alternative representations of Type 3 languages that may be significantly more concise than other models that share the same express- ing power. The goal of this work is to provide an overview of old and recent re- sults on these formal systems from a descriptional complexity perspective, that is the study of the relationships between the sizes of such devices. We also present some results related to the investigation of the famous ques- tion posed by Sakoda and Sipser in 1978, concerning the size blowups from nondeterministic finite automata to two-way deterministic finite automata.
25 Apr 2020
TL;DR: This paper proposes a new class of bounded underapproximations for multi-pushdown systems, which subsumes most existing classes and develops an efficient algorithm for solving the under-approximate reachability problem, based on efficient fix-point computations.
Abstract: Boolean programs with multiple recursive threads can be captured as pushdown automata with multiple stacks. This model is Turing complete, and hence, one is often interested in analyzing a restricted class which still captures useful behaviors. In this paper, we propose a new class of bounded underapproximations for multi-pushdown systems, which subsumes most existing classes. We develop an efficient algorithm for solving the under-approximate reachability problem, which is based on efficient fix-point computations. We implement it in our tool BHIM and illustrate its applicability by generating a set of relevant benchmarks and examining its performance. As an additional takeaway BHIM solves the binary reachability problem in pushdown automata. To show the versatility of our approach, we then extend our algorithm to the timed setting and provide the first implementation that can handle timed multi-pushdown automata with closed guards.
Posted Content•
TL;DR: It is decidable for deterministic visibly push-down automata whether there exists a synchronizing word with each of these stack constraints, i.e., the problems are in EXPTIME.
Abstract: We generalize the concept of synchronizing words for finite automata, which map all states of the automata to the same state, to deterministic visibly push-down automata. Here, a synchronizing word w does not only map all states to the same state but also fulfills some conditions on the stack content of each run after reading w. We consider three types of these stack constraints: after reading w, the stack (1) is empty in each run, (2) contains the same sequence of stack symbols in each run, or (3) contains an arbitrary sequence which is independent of the other runs. We show that in contrast to general deterministic push-down automata, it is decidable for deterministic visibly push-down automata whether there exists a synchronizing word with each of these stack constraints, i.e., the problems are in EXPTIME. Under the constraint (1) the problem is even in P. For the sub-classes of deterministic very visibly push-down automata the problem is in P for all three types of constraints. We further study variants of the synchronization problem where the number of turns in the stack height behavior caused by a synchronizing word is restricted, as well as the problem of synchronizing a variant of a sequential transducer, which shows some visibly behavior, by a word that synchronizes the states and produces the same output on all runs.
Posted Content•
TL;DR: The results obtained here provide all necessary tools for an in-depth study of logical properties of trees generated by collapsible pushdown automata/recursion schemes.
Abstract: This paper studies a large class of two-player perfect-information turn-based parity games on infinite graphs, namely those generated by collapsible pushdown automata. The main motivation for studying these games comes from the connections from collapsible pushdown automata and higher-order recursion schemes, both models being equi-expressive for generating infinite trees. Our main result is to establish the decidability of such games and to provide an effective representation of the winning region as well as of a winning strategy. Thus, the results obtained here provide all necessary tools for an in-depth study of logical properties of trees generated by collapsible pushdown automata/recursion schemes.
[...]
TL;DR: This new version of Automata Tutor supports automated grading and feedback generation for a greatly extended variety of new problems, including problems that ask students to create regular expressions, context-free grammars, pushdown automata and Turing machines corresponding to a given description.
Abstract: Computer science class enrollments have rapidly risen in the past decade. With current class sizes, standard approaches to grading and providing personalized feedback are no longer possible and new techniques become both feasible and necessary. In this paper, we present the third version of Automata Tutor, a tool for helping teachers and students in large courses on automata and formal languages. The second version of Automata Tutor supported automatic grading and feedback for finite-automata constructions and has already been used by thousands of users in dozens of countries. This new version of Automata Tutor supports automated grading and feedback generation for a greatly extended variety of new problems, including problems that ask students to create regular expressions, context-free grammars, pushdown automata and Turing machines corresponding to a given description, and problems about converting between equivalent models - e.g., from regular expressions to nondeterministic finite automata. Moreover, for several problems, this new version also enables teachers and students to automatically generate new problem instances. We also present the results of a survey run on a class of 950 students, which shows very positive results about the usability and usefulness of the tool.
TL;DR: This study has modeled chemical reactions using two-way quantum finite automata, which are halted in linear time, and it has been proven that computational versatility can be increased by combining chemical accept/reject signatures and quantum automata models.
Abstract: In recent years, the modeling interest has increased significantly from the molecular level to the atomic and quantum scale. The field of computational chemistry plays a significant role in designing computational models for the operation and simulation of systems ranging from atoms and molecules to industrial-scale processes. It is influenced by a tremendous increase in computing power and the efficiency of algorithms. The representation of chemical reactions using classical automata theory in thermodynamic terms had a great influence on computer science. The study of chemical information processing with quantum computational models is a natural goal. In this paper, we have modeled chemical reactions using two-way quantum finite automata, which are halted in linear time. Additionally, classical pushdown automata can be designed for such chemical reactions with multiple stacks. It has been proven that computational versatility can be increased by combining chemical accept/reject signatures and quantum automata models.
01 Jan 2020
TL;DR: In weighted automata theory, many classical results on formal languages have been extended into a quantitative setting and it is shown that (mixed) ω-algebraic systems can be transformed into Greibach normal form, which generalize fundamental properties of context-free languages to weighted context- free languages.
Abstract: In weighted automata theory, many classical results on formal languages have been extended into a quantitative setting. Here, we investigate weighted context-free languages of infinite words, a generalization of ω-context-free languages (Cohen, Gold 1977) and an extension of weighted context-free languages of finite words (Chomsky, Schützenberger 1963). As in the theory of formal grammars, these weighted context-free languages, or ω-algebraic series, can be represented as solutions of mixed ω-algebraic systems of equations and by weighted ω-pushdown automata. In our first main result, we show that (mixed) ω-algebraic systems can be transformed into Greibach normal form. We use the Greibach normal form in our second main result to prove that simple ω-reset pushdown automata recognize all ω-algebraic series. Simple ω-reset automata do not use -transitions and can change the stack only by at most one symbol. These results generalize fundamental properties of context-free languages to weighted context-free languages.
Posted Content•
TL;DR: The ω-powers appear very naturally in Theoretical Computer Science in the characterization of several classes of languages of infinite words accepted by various kinds of automata, like Buchi automata or Buchi pushdown automata.
Abstract: The ω-power of a finitary language L over a finite alphabet Σ is the language of infinite words over Σ defined by L ∞ := {w 0 w 1. .. ∈ Σ ω | ∀i ∈ ω w i ∈ L}. The ω-powers appear very naturally in Theoretical Computer Science in the characterization of several classes of languages of infinite words accepted by various kinds of automata, like Buchi automata or Buchi pushdown automata. We survey some recent results about the links relating Descriptive Set Theory and ω-powers.
24 Aug 2020
TL;DR: In this article, the complexity of language operations on straight line programs (SLP) was studied and it was shown that the complexity is exponential for intersection and shuffle, and double exponential for complementation.
Abstract: A straight line program (SLP) is a circuit with letters as inputs and gates performing one of the operations union, concatenation, or star; its size is the number of its nodes. Every SLP describes a regular language in a natural manner. We study the complexity of language operations on SLPs and show that the complexity is exponential for intersection and shuffle, and double exponential for complementation. These results carry over to constant height pushdown automata and non-self-embedding grammars, since these models and SLPs are polynomially equivalent. We also examine extended SLPs that may perform additional operations and show that the cost of simulating an extended SLP with shuffle or intersection by a conventional SLP is double exponential.
Posted Content•
TL;DR: In this paper, the authors have modeled chemical reactions using two-way quantum finite automata, which are halted in linear time and classical pushdown automata can be designed for such chemical reactions with multiple stacks.
Abstract: In recent years, the modeling interest has increased significantly from the molecular level to the atomic and quantum scale. The field of computational chemistry plays a significant role in designing computational models for the operation and simulation of systems ranging from atoms and molecules to industrial-scale processes. It is influenced by a tremendous increase in computing power and the efficiency of algorithms. The representation of chemical reactions using classical automata theory in thermodynamic terms had a great influence on computer science. The study of chemical information processing with quantum computational models is a natural goal. In this paper, we have modeled chemical reactions using two-way quantum finite automata, which are halted in linear time. Additionally, classical pushdown automata can be designed for such chemical reactions with multiple stacks. It has been proven that computational versatility can be increased by combining chemical accept/reject signatures and quantum automata models.
Posted Content•
TL;DR: This article studies the logical properties of a very general class of infinite ranked trees, namely, those generated by higher-order recursion schemes, and provides an effective solution to three main problems: model-checking, logical reflection, and selection.
Abstract: This paper studies the logical properties of a very general class of infinite ranked trees, namely those generated by higher-order recursion schemes. We consider, for both monadic second-order logic and modal mu-calculus, three main problems: model-checking, logical reflection (aka global model-checking, that asks for a finite description of the set of elements for which a formula holds) and selection (that asks, if exists, for some finite description of a set of elements for which an MSO formula with a second-order free variable holds). For each of these problems we provide an effective solution. This is obtained thanks to a known connection between higher-order recursion schemes and collapsible pushdown automata and on previous work regarding parity games played on transition graphs of collapsible pushdown automata.
01 Jan 2020
TL;DR: In this article, it was shown that the synchronizability problem for deterministic push-down automata is undecidable even when looking at deterministic one-counter automata.
Abstract: The question if a deterministic finite automaton admits a software reset in the form of a so-called synchronizing word can be answered in polynomial time. In this paper, we extend this algorithmic question to deterministic automata beyond finite automata. We prove that the question of synchronizability becomes undecidable even when looking at deterministic one-counter automata. This is also true for another classical mild extension of regularity, namely that of deterministic one-turn push-down automata. However, when we combine both restrictions, we arrive at scenarios with a PSPACE-complete (and hence decidable) synchronizability problem. Likewise, we arrive at a decidable synchronizability problem for (partially) blind deterministic counter automata.
There are several interpretations of what synchronizability should mean for deterministic push-down automata. This is depending on the role of the stack: should it be empty on synchronization, should it be always the same or is it arbitrary? For the automata classes studied in this paper, the complexity or decidability status of the synchronizability problem is mostly independent of this technicality, but we also discuss one class of automata where this makes a difference.
TL;DR: The goal of the paper is to bridge tractable formalisms specialized for expressing separately dense-time real-time properties and context-free properties though preserving tractability in the combined setting.
Abstract: The paper focuses on automata and linear temporal logics for real-time pushdown reactive systems bridging tractable formalisms specialized for expressing separately dense-time real-time properties and context-free properties though preserving tractability. As for automata, we introduce Event-Clock Nested Automata ( ECNA ), a formalism that combines Event Clock Automata ( ECA ) and Visibly Pushdown Automata ( VPA ). ECNA enjoy the same closure and decidability properties of ECA and VPA expressively extending any previous attempt of combining ECA and VPA . As for temporal logics, we introduce two formalisms for specifying quantitative timing context-free requirements: Event-Clock Nested Temporal Logic ( EC_NTL ) and Nested Metric Temporal Logic ( NMTL ). EC_NTL is an extension of both the logic CaRet and Event-Clock Temporal Logic having Exptime -complete satisfiability of EC_NTL and visibly model-checking of Visibly Pushdown Timed Systems ( VPTS ) against EC_NTL . NMTL is a context-free extension of standard Metric Temporal Logic ( MTL ) which is in general undecidable having, though, a fragment expressively equivalent to EC_NTL with Exptime -complete satisfiability and visibly model-checking of VPTS problems.
11 May 2020
TL;DR: A detailed characterization of the accept and strong space complexity measures for checking stack automata is given, and an investigation is done regarding the best complexity of any machine accepting a given language, and on decidability of space complexity properties.
Abstract: This paper examines several measures of space complexity on variants of stack automata: non-erasing stack automata and checking stack automata. These measures capture the minimum stack size required to accept any word in a language (weak measure), the maximum stack size used in any accepting computation on any accepted word (accept measure), and the maximum stack size used in any computation (strong measure). We give a detailed characterization of the accept and strong space complexity measures for checking stack automata. Exactly one of three cases can occur: the complexity is either bounded by a constant, behaves (up to small technicalities explained in the paper) like a linear function, or it grows arbitrarily larger than the length of the input word. However, this result does not hold for non-erasing stack automata; we provide an example when the space complexity grows with the square root of the input length. Furthermore, an investigation is done regarding the best complexity of any machine accepting a given language, and on decidability of space complexity properties.