Showing papers on "Pushdown automaton published in 1979"

Tree-Size Bounded Alternation

Abstract: The size of an accepting computation tree of an alternating Turing machine (ATM) is introduced as a complexity measure. We present a number of applications of tree-size to the study of more traditional complexity classes. Tree-size on ATMs is shown to closely correspond to time on nondeterministic TMs and on nondeterministic auxiliary pushdown automata. One application of the later is a useful new characterization of the class of languages log-space-reducible to context-free languages. Surprising relationships with parallel-time complexity are also demonstrated. ATM computations using at most space S(n) and tree-size Z(n) (simultaneously) can be simulated in alternating space S(n) and time S(n) · log Z(n) (simultaneously). Several well-known simulations, e.g., Savitch's theorem, are special cases of this result. It also leads to improved parallel complexity bounds for many problems in terms of both time and number of “processors.” As one example we show that context-free language recognition in time O(log2 n) is possible on several parallel models. Further, this bound is achievable with only a polynomial number of processors, in contrast to all previously known sub-linear time CFL recognizers.

Noncanonical SLR(1) Grammars

Abstract: Two noncanonical extensions of the simple LR(1) (SLR(1)) method are presented, which reduce not only handles but also other phrases of sentential forms. A class of context-free grammars called leftmost SLR(1) (LSLR(1)) is defined by using lookahead symbols which appear in leftmost derivations. This class includes the SLR(1), reflected SMSP, and total precedence grammars as proper subclasses. The class of LSLR(1) languages properly includes the deterministic context-free languages, their reflections, and total precedence languages. By requiring that phrases which have been scanned be reduced as early as possible, a larger class of context-free grammars called noncanonical SLR(1) (NSLR(1)) is defined. The NSLR(1) languages can be recognized deterministically in linear time using a two-stack pushdown automaton. An NSLR(1) parser generator has been implemented. Empirical results show that efficient NSLR(1) parsers can be constructed for some non-LR grammars which generate nondeterministic languages. Applications of the NSLR(1) method to improve the parsing and translation of programming languages are discussed.

Linearity is polynomially decidable for realtime pushdown store automata

Abstract: If M is a realtime deterministic pushdown store acceptor, the language L ( M ) accepted by M by final state and empty store is linear context-free if and only if a certain grammar obtained from M is linear context-free. Hence, it is polynomially decidable for realtime deterministic pushdown store automata M whether L(M) is linear context-free. If M is a realtime deterministic pushdown store acceptor and L ( M ) is linear context-free, we can construct a realtime single turn deterministic pushdown store automaton {if27-1} with {if27-2}. Hence “ L ( M ) = L ” is decidable for M a realtime deterministic pushdown store acceptor and L the language accepted by final state by a single turn deterministic pushdown store acceptor.

On relativizing auxiliary pushdown machines

Abstract: We consider relativizing the constructions of Cook in [4] characterizing space-bounded auxiliary pushdown automata in terms of timebounded computers. LetS(n) ≥ logn be a measurable space bound. LetDTA[NTA] be the class of setsS such that there exists a machineM such thatM with oracleA recognizes the setS andM is a deterministic [nondeterministic] oracle Turing machine acceptor that runs in time 2cS(n) for some constantc. LetDBiA[NBiA] be the class of setsS such that there exists a machineM such thatM with oracleA recognizes the setS andM is a deterministic [non-deterministic] oracle Turing machine acceptor with auxiliary pushdown that runs in spaceS(n) and never queries the oracle about strings longer than:S(n) ifi = 1, 2cS(n) for some constantc, ifi = 2, + ∞ ifi = 3.

Strict Deterministic Languages and Controlled Rewriting Systems

Abstract: A controlled rewriting system over an alphabet X is a finite set of rules vi → wi (l⩽i⩽n) with vi , wi in X* such that |vi|<|wi| , each rule being associated with a regular language Ri X* Given such a system, f ⇒ g means that f=αviβ and g=αwiβ for some i, α in Ri , β in X* The system is said to be injective if and only if f ⇒ g ⇐ f′ implies f=f′ Controlled rewriting systems are a special case of finite relations with computable left context (P Butzbach [5], 1973), which can be defined as above, with the Ri's recursive instead of regular P Butzbach proved [5] that every simple deterministic language [11] is generated by some finite relation with computable left context iterating from a finite set of words Here we improve this result with our THEOREM 1 : "Every strict deterministic language is generated by some injective controlled rewriting system iterating from a finite set of words" Moreover, let A be a deterministic pushdown automaton and ⇒ be the rewriting relation associated with A by the above theorem Let θ : X* ⇒ X* defined by θ(u)=v if and ∃ w, w ⇒ v (v is unique, for ⇒ is injective); in some sense, θ generalizes the semi-Dyck simplification We state :

On the Succintness of Different Representations of Languages

Abstract: The purpose of this paper is to give simple new proofs of some interesting recent results about the relative succinctness of different representations of regular, deterministic and unambiguous context-free languages and to derive some new results about how the relative succinctness of representations change when the representations contain a formal proof that the languages generated are in the desired subclass of languages.

New proofs for jump dpda's

Abstract: The deterministic context-free languages (see e.g. Harrison [5]) constitute an important subfamily of the context-free languages. The need of good parsing algorithms and the intriguing equivalence problem have lead to the investigation of various subfamilies and various characterizations of this family. The deterministic pushdown automata with jumps, jump dpda's in short, establish a useful device of characterizing the deterministic languages.