Real-time Deterministic Pushdown Automata Research Articles

Generating fluent embedded domain-specific languages with subchaining

This paper presents Silverchain, a tool that generates a fluent embedded domain-specific language (EDSL) from a BNF-style grammar. A fluent EDSL is a class library that allows its users to embed domain-specific sentences into a program written in a general-purpose language by method chaining. A generated EDSL is designed so that its users can find syntactic errors from type errors and make effective use of method chaining in various situations. The first feature is realized by setting the return type of each method based on which methods may be invoked next, and the second feature is achieved by providing subchaining APIs besides regular chaining APIs. The contribution of this paper is the development of a translation method from a grammar to such an EDSL. Our translation method is modeled as the construction of a set of single-state real-time deterministic pushdown automata (RPAs). A fluent EDSL is obtained by encoding those RPAs into class definitions. In the construction of RPAs, Silverchain does not add or remove any non-terminal from the given grammar. This constraint is required to generate subchaining APIs as specified in the grammar.

From Security Protocols to Pushdown Automata

Formal methods have been very successful in analyzing security protocols for reachability properties such as secrecy or authentication. In contrast, there are very few results for equivalence-based properties, crucial for studying, for example, privacy-like properties such as anonymity or vote secrecy. We study the problem of checking equivalence of security protocols for an unbounded number of sessions. Since replication leads very quickly to undecidability (even in the simple case of secrecy), we focus on a limited fragment of protocols (standard primitives but pairs, one variable per protocol’s rules) for which the secrecy preservation problem is known to be decidable. Surprisingly, this fragment turns out to be undecidable for equivalence. Then, restricting our attention to deterministic protocols, we propose the first decidability result for checking equivalence of protocols for an unbounded number of sessions. This result is obtained through a characterization of equivalence of protocols in terms of equality of languages of (generalized, real-time) deterministic pushdown automata. We further show that checking for equivalence of protocols is actually equivalent to checking for equivalence of generalized, real-time deterministic pushdown automata. Very recently, the algorithm for checking for equivalence of deterministic pushdown automata has been implemented. We have implemented our translation from protocols to pushdown automata, yielding the first tool that decides equivalence of (some class of) protocols, for an unbounded number of sessions. As an application, we have analyzed some protocols of the literature including a simplified version of the basic access control (BAC) protocol used in biometric passports.

An approach to deciding the observational equivalence of Algol-like languages

We prove that the observational equivalence of third-order finitary (i.e. recursion-free) Idealized Algol (IA) is decidable using Game Semantics. By modelling the state explicitly in our games, we show that the denotation of a term M of this fragment of IA is a compactly innocent strategy-with-state, i.e. the strategy is generated by a finite view function f M . Given any such f M , we construct a real-time deterministic pushdown automaton (DPDA) that recognizes the complete plays of the knowing-strategy denotation of M. Since such plays characterize observational equivalence, and there is an algorithm for deciding whether any two DPDAs recognize the same language, we obtain a procedure for deciding the observational equivalence of third-order finitary IA. Restricted to second-order terms, the DPDA representation cuts down to a deterministic finite automaton; thus our approach gives a new proof of Ghica and McCusker’s regular-expression characterization for this fragment. Our algorithmic representation of program meanings, which is compositional, provides a foundation for model-checking a wide range of behavioural properties of IA and other cognate programming languages. Another result concerns second-order IA with full recursion: we show that observational equivalence for this fragment is undecidable.

Equivalence of real‐time DPDAs and discrete extended simple recurrent networks with some restrictions

AbstractTo model human natural language processing using computation theory, Elman proposed a simple recurrent network. A simple recurrent network is a recurrent neural network with restrictions added to the connections between gates. When the range of the function for computing each gate of a simple recurrent network is a finite set (this is called a discrete simple recurrent network), its computational capability is known to be equivalent to that of a finite automaton with output. This paper introduces a modification of a discrete simple recurrent network so that it has a computational capability equivalent to that of a real‐time deterministic pushdown automaton (real‐time DPDA). In other words, the discrete simple recurrent network is extended as follows. (1) It contains a number of gates equal to a constant multiple of the input length, and (2) those gates can be used to simulate a stack with a depth of at most the input length. © 2003 Wiley Periodicals, Inc. Syst Comp Jpn, 34(7): 55–62, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/scj.10275

Constructing a realtime deterministic pushdown automaton from a grammar

A new direct construction from a grammar to a realtime deterministic pushdown automation is presented. The grammar is required to be in a special form, but the construction is more natural than previously known constructions. As a result the family of stack uniform strict deterministic languages can be characterized by a grammar family.

A pushdown automation or a context-free grammar—which is more economical?

For every pair of positive integers n and p, there is a language accepted by a real-time deterministic pushdown automaton with n states and p stack symbols and size O( np), for which every context-free grammar needs at least n 2 p+1 nonterminals if n>1 (or p non-terminals if n = 1). It follows that there are context-free languages which can be recognized by pushdown automata of size O( np), but which cannot be generated by context-free grammars of size smaller than O( n 2 p); and that the standard construction for converting a pushdown automaton to a context-free grammar is optimal in the sense that it infinitely often produces grammars with the fewest number of nonterminals possible.

A real-time strictness test for deterministic pushdown automata

A context-free language is said to be real-time strict if it is accepted by a real-time deterministic pushdown automaton with empty stack acceptance. This paper proves that there exists an effective procedure for deciding whether the language accepted by a deterministic pushdown automaton (dpda) is real-time strict. The result implies the following: For any subclass ℰ of real-time dpda's with empty stack acceptance, the problem for deciding whether a dpda is equivalent to some machine in ℰ reduces to that for deciding whether a real-time dpda with empty stack acceptance is equivalent to some machine in ℰ.

Two decidability results for deterministic pushdown automata

A real-time deterministic pushdown automaton is said to be stack uniform if for each input letter a, every a-tule has the same effect on the length of the pushdown store, i.e., if ( s 1 , A) → a ( S 2, w) and ( s 1′ , A′) → a ( s 2′ , w′) are two a-rules, then the lengths of w and w′ are equal. It is shown that the equivalence problem for stack uniform automata and the inclusion problem for stack uniform automata with empty store acceptance are decidable.