Semantics. Expressions reduce according to a call-by-value strategy, for which we define evaluation contexts thus:
Semantics. SECA comes with four semantics, for different purposes. The standard xxxxx- tics defines how programs are executed. The energy-aware semantics addition- ally traces the energy consumption during program execution in a skyline. The symbolic execution semantics executes all possible paths through a program. The energy-aware symbolic execution semantics traces all possible skylines a program can produce. The focus of this paper is the last one; the others are formally defined in a technical report [19]. Below, we will informally discuss the energy-aware semantics, as it is a useful foundation to understand the energy- aware symbolic execution semantics.
Semantics. Figure 3 defines the semantic domains and the inference rules for a big-step evaluation judgment of the form x, R, W € H; u; e ‹→ Hj; uj; v ∈ R W R W This judgment declares that given a variable environment ρ and indexed collections and of read and write permissions, the expression e transforms the initial heap H to the final xxxx Xx and returns value v. Furthermore, it threads a time stamp u, uj Stamp that is incremented at each property write operation and at each permit expression. The permission collections and are indexed by the time stamps of the heaps for which the permissions were granted. The time stamp of a permission uniquely identifies different executions of permit expressions and determines their relative order with respect to heap modifications. ∈ M M A value v Val is either a reference or a closure consisting of an environment and a lambda expression. The representation of a reference is a pair of a heap address A and a collection of access paths, indexed by time stamps. The collection records all permitted access paths that have been traversed during evaluation so far to obtain this reference value. The indexing is again used for marking modifications with time stamps. This representation is dictated by the design choice of path dependency (see Sec. 2.1). A heap maps a location to an object and an object maps a property name to a pair of a time stamp and a value. The time stamp indicates the time of the write operation that last assigned the property. It is required to implement the “sticky update” from Sec. 2.4. x, R, W € H; u; e0 ‹→ H ; u ; (ρ , λx.e) ρ, R, W € Hj; uj; e1 ‹→ Hjj; ujj; v1 ρj[x ›→ v1], R, W € Hjj; ujj; e ‹→ Hjjj; ujjj; v x, R, W € H; u; e0(e1) ‹→ Hjjj; ujjj; v NEW A ∈/ dom(H) ρ, R, W € H; u; new ‹→ H[A ›→ ∅]; u; (A, ∅) PUT x, R, W € H; u; e1 ‹→ Hj; uj; (A, M) x, R, W € Hj; uj; e2 ‹→ Hjj; ujj; v W €chk M.p Hjjj = Hjj[A ›→ Hjj(A)[p ›→ (ujj, v)]] x, R, W € H; u; e1.p := e2 ‹→ Hjjj; ujj + 1; v GET x, R, W € H; u; e ‹→ Hj; uj; (A, M) R €chk M.p < x, R, W € H; u; e.p ‹→ Hj; uj; M.p Hj(A)(p) PERMIT ρj, R[u ›→ Lr ], W[u ›→ Lw ] € H; u + 1; e ‹→ Hj; uj; v ρj = ρ[x ›→ ρ(x) a [u ›→ ε]] x, R, W € H; u; permit x : Lr, Lw in e ‹→ Hj; uj; v
Semantics. This section discusses the semantics of the flow language and the way to integrate it with Event-B. In particular we show how to reason about flow and machine consistency in the terms of machine properties rather than flow or machine traces. But first we use the traces semantics to formally integrate flows with Event-B. The following defines the traces of a flow expression. traces(jskip) = {()} bj j n traces(jstart) = {(jstart)} traces( stop) = {s | n ∈ N ∧ s ≤ ( stop) } b {( )} traces(ei.a) traces(p; q) traces(p|q) traces(∗(p)) traces(pǁEq) = ei.a b {s z | s z ∈ traces(p) ∧ z = ( stop)}∪ = ^ ^ j {s^t | s^z ∈ traces(p) ∧ t ∈ traces(q) ∧ z =ƒ (jstop)} b = traces(p) ∪ traces(q) b | ∗ = traces(p (p; (p))) =b {S(sǁEt | s ∈ traces(p) ∧ t ∈ traces(q)} Here s t states that trace s is a prefix of trace t; α(x) is an alphabet of x (set of all events occurring in x). The parallel composition operator is defined as a collection of possible event interleavings:
Semantics. The semantics of the language of agreements L is based on a possible worlds model We rst de ne a class of models M De nition M hW i is a tuple associating the possible multi agent world states W a function that assigns truth values to formulae and an acces sibility relation associated to programs Now focusing on the actions performed by agents within a multi agent system we de ne the set of paths along which the state of the multi agent system may pass This set of paths is used to de ne our notion of commitment i e what it means for an agent to be bound to uphold an agreement see constraints " in table and s t i i g
Semantics. The semantics of a data signature sig = (S, F ), i.e., the values in its sorts, is constituted by equivalence classes of ground terms. The value of a ) ) ground term t denoted t , is defined by t = {t′ | t′ ≡ t}. Here, we assume an equivalence on ground terms, ( ) ( ), which is sort-safe: if t1 t2 then sortt(t1)= sortt(t2). Such an equivalence could be specified as a set of equations (equational specification [7]) or as a set of rewrite rules. ) The semantics of a data signature sig = (S, F ) is then the multi-sorted initial algebra = ( s s S , ƒf f F ), where s = t t s( ) is the set of values of sort s; and for each function symbol ( f :: s1,..., sn s ) F there is a function ƒf : s1 ... sn s defined by ƒf ( t1 ,..., tn )= f (t1,..., tn) , where t1,..., tn are ground terms of sorts s1,..., sn, respectively. The set of all possible values is = s s S . Function sortv : S gives the sort of a value; it is extended to sequences of values as usual. A valuation for X X is a function assigning values to variables: ϑ : X , which is sort-safe: sortt(x) = sortv(ϑ(x)). The set of all valuations for X is denoted UX . The extension to evaluate terms based on a valuation ϑ is called a term evaluation and denoted by ϑT : T (X) → U . It is defined as ϑT (x) = ϑ(x) and ϑT (f (t1,..., tn)) =ƒf (ϑT (t1),..., ϑT (tn)). For a sequence of distinct variables x¯ = x0 ... xn ∈ X∗ and a sequence of values w¯ = w0 ... wn ∈ U∗, we denote with x¯ w¯ the valuation in U{x0 ,...,xn} defined by (x¯ w¯)(xi) = wi for all 0 ≤ i ≤ n. The semantics of a ground term mapping m ∈ T (∅)X is the valuation m defined as m (x)= m(x) for all x ∈ X. ) ) ) In our test algorithm, we need to represent the values in a valuation ϑ ∈ UX (tmap(ϑ))(x)= t ⇒ ϑ(x)= t), for all x ∈ X. as terms again. We therefore use any term mapping tmap(ϑ) ∈T (∅)X satisfying For sort Bool we assume that ) ) interprets ground terms in TBool(∅) as usual, e.g., True = true. Boolean terms can be seen as formulas, for which we can consider their satisfiability. A Boolean term t ∈ TBool(X) is satisfiable if there exists a valuation ϑ vars(t) such that ϑT (t) = true. Satisfiability, however, is undecidable in general. Hence, a tool solving satisfiability problems in our algorithms may return ‘unknown’. Therefore we will distinguish explicitly between semantic satisfiability and a tool solver, with solver(t) returning either sat, unsat, or unknown. Moreover, we assume that solver allows to retrieve a valuation that witnesses satisfiabilit...
Semantics. AVCConfig – SHALL contain sufficient sequenceParameterSetNALUnit and pictureParameterSetNALUnit entries to describe the configurations of all samples referenced by the current track fragment. Note: AVCDecoderConfigurationRecord contains a table of each unique Sequence Parameter Set NAL unit and Picture Parameter Set NAL unit referenced by AVC Slice NAL Units contained in samples in this track fragment. As defined in [ISOAVC] Section 5.2.4.1.2 semantics: • sequenceParameterSetNALUnit contains a SPS NAL Unit, as specified in [H264]. SPSs shall occur in order of ascending parameter set identifier with gaps being allowed. • pictureParameterSetNALUnit contains a PPS NAL Unit, as specified in [H264]. PPSs shall occur in order of ascending parameter set identifier with gaps being allowed.
Semantics baseLocation – SHALL contain the Base Location defined in Section 8.3.2 of [DSystem], encoded as a string of ASCII bytes as defined in [ASCII], followed by null bytes (0x00) to a length of 256 bytes. • purchaseLocation – MAY contain the Purchase Location defined in Section 8.3.3 of [DSystem], encoded as a string of ASCII bytes as defined in [ASCII], followed by null bytes (0x00) to a length of 256 bytes. If no Purchase Location is included, this field SHALL be filled with null bytes (0x00). • Reserved – Reserve space for future use. Implementations conformant with this specification SHALL ignore this field.
Semantics. All of the semantics of version zero (0) of this box, as defined in [ISO], apply to this version of the box with the following additional semantics specifically for SubtitleSampleEntry():
Semantics flags is inherited from the FullBox structure. The SampleEncryptionBox currently supports the following bit values: 0x2 – UseSubSampleEncryption If the UseSubSampleEncryption flag is set, then the track fragment that contains this Sample Encryption Box SHALL use the sub-sample encryption as described in Section 3.2. When this flag is set, sub-sample mapping data follows each InitilizationVector. The sub-sample mapping data consists of the number of sub- samples for each sample, followed by an array of values describing the number of bytes of clear data and the number of bytes of encrypted data for each sub-sample. • sample_count is the number of encrypted samples in this track fragment. This value SHALL be either zero (0) or the total number of samples in the track fragment. • InitializationVector specifies the initialization vector (IV) needed for decryption of a sample. InitializationVector semantics SHALL conform to the semantics defined in [ISO] Annex I 7.2. IV_size SHALL be taken as the value in the corresponding Track Encryption Box (‘tenc’). The nth InitializationVector in the table SHALL be used for the nth sample in the track fragment. Selection of InitializationVector values SHOULD follow the recommendations of [ISO] Annex I 7.4. See Section 3.2 for further details on how encryption is applied. • subsample_count specifies number of sub-sample encryption entries present for this sample. • BytesOfClearData specifies number of bytes of clear data at the beginning of this sub- sample encryption entry. (Note, that this value can be zero if no clear bytes exist for this entry.) • BytesOfEncryptedData specifies number of bytes of encrypted data following the clear data. (Note, that this value can be zero if no encrypted bytes exist for this entry.) The sub-sample encryption entries SHALL NOT include an entry with a zero value in both the BytesOfClearData field and in the BytesOfEncryptedData field. The total length of all BytesOfClearData and BytesOfEncryptedData for a sample SHALL equal the length of the sample. Further, it is recommended that the sub- sample encryption entries be as compactly represented as possible. For example, instead of two entries with {15 clear, 0 encrypted}, {17 clear, 500 encrypted} use one entry of {32 clear, 500 encrypted}
