Mamoru Fujii

On multiple context-free grammars

Abstract Multiple context-free grammars (mcfgs) is a subclass of generalized context-free grammars introduced by Pollard (1984) in order to describe the syntax of natural languages. The class of languages generated by mcfgs (called multiple context-free languages or, shortly, mcfls) properly includes the class of context-free languages and is properly included in the class of context-sensitive languages. First, the paper presents results on the generative capacity of mcfgs and also on the properties of mcfls such as formal language-theoretic closure properties. Next, it is shown that the time complexity of the membership problem for multiple context-free languages is O(ne), where n is the length of an input string and e is a constant called the degree of a given mcfg. Head grammars (hgs) introduced by Pollard and tree adjoining grammars (tags) introduced by Joshi et al. (1975) are also grammatical formalisms to describe the syntax of natural languages. The paper also presents the following results on the generative capacities of hgs, tags and 2-mcfgs, which are a subclass of mcfgs: (1) The class HL of languages generated by hgs is the same as the one generated by tags; (2) HL is the same as the one generated by left-wrapping hgs (or right-wrapping hgs) which is a proper subclass of hgs; (3) HL is properly included in the one generated by 2-mcfgs. As a corollary of (1), it is also shown that HL is a substitution-closed full AFL.

Generalized context-free grammars and multiple context-free grammars

It is shown that the class of languages generated by generalized context-free grammars (gcfgs) introduced by Pollard is exactly the class of recursively enumerable sets. Next, a subclass of gcfgs called multiple context-free grammars (mcfgs) is introduced and it is shown that the class of languages generated by mcfgs properly contains the class of context-free languages and is properly contained in the class of context-sensitive languages. In mcfgs, it is possible to account for structures involving discontinuous constituents in a particularly simple manner. Such concepts as phrase structure and derivation tree in context-free grammars (cfgs) can be extended naturally in mcfgs. Furthermore, the class of languages generated by mcfgs enjoys the formal language-theoretic closure properties that the class of context-free languages does.

A Verification Procedure via Invariant for Extended Communicating Finite-State Machines

This paper presents a method for verifying safety property of a communication protocol modeled as two extended communicating finite-state machines with two unbounded FIFO channels connecting them. In this method, four types of atomic formulae specifying a condition on a machine and a condition on a sequence of messages in a channel are introduced. A human verifier describes a logical formula which expresses conditions expected to be satisfied by all reachable global states, and a verification system proves that the formula is indeed satisfied by such states (i.e. the formula is an invariant) by induction. If the invariant is never satisfied in any unsafe state, it can be concluded that the protocol is safe. To show the effectiveness of this method, a sample protocol extracted from the data transfer phase of the OSI session protocol was verified by using the verification system.

Quantifying a design process based on experiments

The authors identify important factors that quantify the software design process, by which they mean the phase of software development that spans the specification and coding,. Through two experiments using student subjects. They identify the quality of the specification and programmer effort as important factors. >

A processing system for programming specifications in a natural language

An English-language fragment L/sub NS/, which is used for writing program specifications, is defined using the algebraic language ASL/*. In order to define the semantics of L/sub NS/, the translation from each sentence in L/sub NS/ into a formula in a formal system is defined. If a sentence s in L/sub NS/ is translated into a formula t, then the semantics of s is defined to be the semantics of t in the system. The definition of nonlogical words such as nouns and verbs are given as axioms. A processing system for natural-language specifications that is based on this method has been implemented. Since the number of nonlogical words is very large and their semantics depend on problem domains, it seems to be difficult to define the semantics of all the words from the beginning. The system not only translates specifications into formulas but also supports dictionary expansion. Several specifications have been analyzed using the system, and the nonlogical words have been defined and stored in the dictionary.<<ETX>>

A semi-automated verification method for communication protocols modeled as 2-ECFSMs

Previously, we proposed a verification method via invariants for communication protocol modeled as 2-ECPSMs. In the proposed method, a human verifier describes an invariant of a given protocol in a disjunctive normal form, and a verification system shows safety or liveness based on the invariant. The tedious work on describing invariant formulae is the most significant shortcoming of the proposed method. This paper deals with a semi-automated derivation of invariant formulae for communication protocol modeled as 2-ECFSMs. In the method, the logical formula which holds on a subset of reachable states is automatically generated. Such a subset consists of states which are teachable by synchronous communication from the initial states and those which are reachable by sequences of sending transitions from synchronously reachable states. To obtain an invariant, a human verifier supplements several disjuncts for other part of reachability set. We conducted an experiment on deriving an invariant formula of a sample protocol extracted from the OSI session protocol. By the result, 636 conjunctive formulae were automatically derived and the conjunction of those formulae was shown to be an invariant of the sample protocol, i.e. the sample protocol was shown to be safe automatically.

Logical programming for the telegram analysis problem

Abstract The telegram analysis problem posed by Henderson and Snowdon has been repeatedly taken into account. This paper adds yet another contribution to the literature on this problem. We propose rigorous specification methods, and describe how programs can be derived from BNF to Definite Clause Grammar in Prolog by two different methods. One method is especially useful for large scale problems and has been applied to file manipulation, and the other is applicable to simple problems.

A model of nested transaction with fine granularity of concurrency control

Proposes a new model of nested transactions which achieves higher concurrency of transactions than the traditional model. Most of the previously proposed concurrency control algorithms for nested transactions were based on two-phase locking (2PL). In such algorithms, however, the concurrency of transactions is not so high. To achieve high concurrency, it was decided to apply serialization graph testing (SGT) to the concurrency control of nested transactions. However, in the traditional nested transactions model, the subtransactions dont satisfy the ACID (atomicity, consistency, isolation and durability) properties. We designed our nested transaction model so that each subtransaction satisfies the ACID properties. We considered applying an SGT scheduling algorithm to our model. By scheduling subtransactions as independent transactions, high concurrency can be achieved. However, the usual SGT algorithm causes deadlocks in our model. To avoid these deadlocks, we modified the usual SGT algorithm.

A method for verifying liveness of protocols modeled as a class of ECFSM

In a previous work, we proposed a method for verifying safety of communication protocols modeled as two extended communicating finite-state machines with two unbounded FIFO channels connecting them. This paper presents a method for verifying liveness based on the above method. Liveness is formulated as Q-liveness which states “∀gs ∈ RS ∃gs′ ∈ GS Q {gs′ is reachable from gs}”, where RS and GS Q denote the set of reachable global states and the set of global states satisfying the property Q, respectively. In the proposed verification method, a finite degenerated reachability graph, DRG, of a given protocol is constructed. In DRG, each node represents a subset of reachable states, and if there exists an edge from a node υ i to another node υ j , where υ i and υ j represent subsets of reachable states RS i and RS j respectively, then “∀gs ∈ RS i ∃gs′ ∈ RS j {gs′ is reachable from gs}” holds. By exploring DRG, Q-liveness is shown to hold. An experimental result on verifying liveness of a sample protocol extracted from the data transfer phase of the OSI session protocol, is also described to show the effectiveness of the verification method.

The generative power of multiple context-free grammars and head grammars

Multiple context-free grammars (mcfgs) and head grammars (hgs) are subclasses of generalized context-free grammars introduced by Pollard to describe the syntax of natural languages. In this paper, the following properties of mcfgs and hgs are shown: (1) the class HL of languages generated by hgs is the same as that generated by the tree adjoining grammars introduced by Joshi et al.; (2) HL is the same as that generated by left-wrapping hgs (or right-wrapping hgs) which is a proper subclass of hgs; (3) HL is properly included in the one generated by 2-mcfgs, which is a proper subclass of mcfgs. As a corollary of (1), it is also shown that HL is a substitution closed full AFL.